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Trigonometric identities challenge problems


We have two expressions C and D.
C=tan(40°)csc(40°)csc(50°)sec(60°)D=sin2(15°)+sin2(75°)sin(30°)sin(60°)sin(90°)\begin{aligned} C &= \dfrac{\tan(40\degree)\csc(40\degree)}{\csc(50\degree)\sec(60\degree)}\\\\ D &= \dfrac{\sin^2(15\degree) + \sin^2(75\degree)}{\sin(30\degree)\sin(60\degree)\sin(90\degree)} \end{aligned}
Evaluate left parenthesis, 6, C, plus, square root of, 3, end square root, D, right parenthesis without using a calculator.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text