First slide

Properties of ITF

Question

$C o s [S i n^{- 1} (2 \cos^{2} θ - 1) + C o s^{- 1} (1 - 2 \sin^{2} θ)] =$

Easy

A

0
B

1
C

$- 1$
D

$\frac{π}{2}$

Solution

$W e k n o w t h a t 2 \cos^{2} θ - 1 = 1 - 2 \sin^{2} θ = \cos 2 θ ∴ \cos [\sin^{- 1} (2 \cos^{2} θ - 1) + \cos^{- 1} (1 - 2 \sin^{2} θ)] = \cos [\sin^{- 1} (\cos 2 θ) + \cos^{- 1} (\cos 2 θ)] = \cos [\sin^{- 1} (\sin (\frac{π}{2} - 2 θ)) + \cos^{- 1} (\cos 2 θ)] = \cos (\frac{π}{2} - 2 θ + 2 θ) = 0$

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