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Course: Class 11 math (India) > Unit 3
Lesson 7: Solutions to select NCERT problemsSelect problems from miscellaneous exercise
Solutions to few problems from miscellaneous exercise on class 11 trigo.
In this article we will look at solutions of a few selected problems from miscellaneous exercise on chapter 3 of NCERT.
Problem 1:
Prove that:
Solution:
See the expression on the LHS. How do we start simplifying things? We have a couple of options.
Breakdown using the formula
Or, evaluate using the formula
Let's try the second option.
Now, the LHS becomes
Now recall that . Therefore,
Using this in the expression above, we have
Try to prove this again by proceeding via the first option.
Problem 2:
Prove that:
Solution:
Let's expand the LHS.
Problem 3:
Prove that:
Solution:
How do we make LHS equal to RHS? The most obvious thing which comes to mind is to apply the formula on the LHS.
Let's do that.
Problem 4:
Find , and for the following case:
Solution:
First let's try to find . Why? If we know , we can easily get and by using the identity
After that we can easily find by using .
In given question, lies in quadrant .
So, will lie in quadrant .
Now
Because lies in quadrant , is negative. So, .
Because lies in quadrant , is positive. So, . Similarly,
Because lies in quadrant , is positive. So, .
Finally, .
There is another way to do this problem as well. First we can find by using the identity . And then we can find and from .
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- Didnt quite get the second to last step in problem no 2. Any help please? Thanks.(1 vote)