https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/v/properties-of-itfs 2025-05-22T13:12:03.767544849Z Properties of ITFs In this video, we look at a few properties of inverse trigonometric functions. The first set includes identities where we can cancel out inverse and trig functions. We take a closer look the intervals for which this works. We then look at double and triple angle identities. Here as well, we play close attention to the intervals for which these identities work. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Properties of ITFs In this video, we look at a few properties of inverse trigonometric functions. The first set includes identities where we can cancel out inverse and trig functions. We take a closer look the intervals for which this works. We then look at double and triple angle identities. Here as well, we play close attention to the intervals for which these identities work. https://cdn.kastatic.org/ka-youtube-converted/Tkgx-D38R5w.mp4/Tkgx-D38R5w.mp4 545 Properties of inverse trigonometric functions https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/e/properties-of-itf 2025-05-22T15:18:37.416023755Z Properties of ITF Properties of ITF Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:inverse-trigonometric-functions-ncert-new/x6f66cbee9a2f805b:properties-of-inverse-trigonometric-functions/v/proving-identities-involving-itfs 2025-05-22T13:12:03.767544849Z Proving identities involving ITFs In this video, we prove three results using strategic trigonometric substitutions. We also pay close attention to the intervals for which these results work. The first one relates cos and tan, the second one uses half angle identity for sin, and the third one uses multiple identities including tan of sum of two angles and both variations of cos of twice of an angle. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proving identities involving ITFs In this video, we prove three results using strategic trigonometric substitutions. We also pay close attention to the intervals for which these results work. The first one relates cos and tan, the second one uses half angle identity for sin, and the third one uses multiple identities including tan of sum of two angles and both variations of cos of twice of an angle. https://cdn.kastatic.org/ka-youtube-converted/YVbKVv_JWuQ.mp4/YVbKVv_JWuQ.mp4 747 Properties of inverse trigonometric functions https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/v/using-trig-identities-on-itfs 2025-05-22T13:12:03.767544849Z Using Trig identities on ITFs In this video, we use trigonometric identites to prove 4 results involving addition and subtraction of inverse functions. We leverage different identies for each problem including double angle identites and angle sum identities. The approach for these problems is to start with the side that has multiple angles, apply substitutions and identities to reach the other side. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using Trig identities on ITFs In this video, we use trigonometric identites to prove 4 results involving addition and subtraction of inverse functions. We leverage different identies for each problem including double angle identites and angle sum identities. The approach for these problems is to start with the side that has multiple angles, apply substitutions and identities to reach the other side. https://cdn.kastatic.org/ka-youtube-converted/BcS5f3qX7EA.mp4/BcS5f3qX7EA.mp4 427 Properties of inverse trigonometric functions https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/e/using-trig-identities-on-itfs 2025-05-22T15:18:37.416023755Z Using Trig identities on ITFs Using Trig identities on ITFs Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:inverse-trigonometric-functions-ncert-new/x6f66cbee9a2f805b:properties-of-inverse-trigonometric-functions/v/expressing-inverse-in-simplest-form 2025-05-22T13:12:03.767544849Z Expressing inverse in simplest form In this video, we solve four problems where we express the given inverse function in its simplest form. The approach here is to find the strategic substitutions, apply the relevant identities, and replace the substitutions at the last step. We solve problems where we simplify tan inverse of four different expressions - in x, in cos x, in x and a (for double angle) and in x and a (for triple angle). Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Expressing inverse in simplest form In this video, we solve four problems where we express the given inverse function in its simplest form. The approach here is to find the strategic substitutions, apply the relevant identities, and replace the substitutions at the last step. We solve problems where we simplify tan inverse of four different expressions - in x, in cos x, in x and a (for double angle) and in x and a (for triple angle). https://cdn.kastatic.org/ka-youtube-converted/xDEmRhYkpKo.mp4/xDEmRhYkpKo.mp4 373 Properties of inverse trigonometric functions https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:inverse-trigonometric-functions-ncert-new/x6f66cbee9a2f805b:properties-of-inverse-trigonometric-functions/e/expressing-inverse-in-simplest-form 2025-05-22T15:18:37.416023755Z Expressing inverse in simplest form Expressing inverse in simplest form Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:inverse-trigonometric-functions-ncert-new/x6f66cbee9a2f805b:properties-of-inverse-trigonometric-functions/v/evaluating-compound-itfs 2025-05-22T13:12:03.767544849Z Evaluating compound ITFs In this video, we evaluate compound functions involving inverse trigonometric functions. The approach here is to start from the inner most functions and work our way outwards. We use strategic substitutions and either right angled triangles or relevant trigonometric identities to work things out. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Evaluating compound ITFs In this video, we evaluate compound functions involving inverse trigonometric functions. The approach here is to start from the inner most functions and work our way outwards. We use strategic substitutions and either right angled triangles or relevant trigonometric identities to work things out. https://cdn.kastatic.org/ka-youtube-converted/ojpMkuieL4s.mp4/ojpMkuieL4s.mp4 345 Properties of inverse trigonometric functions https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:inverse-trigonometric-functions-ncert-new/x6f66cbee9a2f805b:properties-of-inverse-trigonometric-functions/e/evaluating-compound-itfs 2025-05-22T15:18:37.416023755Z Evaluating compound ITFs Evaluating compound ITFs Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/v/solving-equations-involving-itfs 2025-05-22T13:12:03.767544849Z Solving equations involving ITFs In this video, we solve three problems having equations involving inverse trigonometric functions. The approach here is to find the strategic substitutions to convert the equation involving inverse trigonometric functions into an equation involving trigonometric functions. We then solve the trigonometric equations for the unknown angle. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Solving equations involving ITFs In this video, we solve three problems having equations involving inverse trigonometric functions. The approach here is to find the strategic substitutions to convert the equation involving inverse trigonometric functions into an equation involving trigonometric functions. We then solve the trigonometric equations for the unknown angle. https://cdn.kastatic.org/ka-youtube-converted/0A9On6iBhPI.mp4/0A9On6iBhPI.mp4 328 Properties of inverse trigonometric functions https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/e/solving-equations-involving-itfs 2025-06-25T14:29:21.853064708Z Solving equations involving ITFs Solving equations involving ITFs Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/e/shifting-angle-to-principal-value-branch 2025-05-05T08:14:25.350149109Z Shifting angle to principal value branch Shift the argument of trigonometric function to find the output. exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:inverse-trigonometric-functions/e/simplify-inverse-trig-function 2025-05-05T08:14:25.350149109Z Simplify inverse trig function Write the given function in the simplest form. exercise