First slide

Properties of ITF

Question

The value of $\sin^{- 1} \{\cot (\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} \frac{\sqrt{12}}{4} + \sec^{- 1} \sqrt{2})\}$ , is

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{6}$
C

0
D

$\frac{π}{2}$

Solution

$\begin{array}{l} \sin^{- 1} \{\cot (\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} \frac{\sqrt{12}}{4} + \sec^{- 1} \sqrt{2})\} \\ = \sin^{- 1} \{\cot (\sin^{- 1} \frac{\sqrt{3} - 1}{2 \sqrt{2}} + \cos^{- 1} \frac{\sqrt{3}}{2} + \sec^{- 1} \sqrt{2})\} \\ = \sin^{- 1} \{\cot (\frac{π}{12} + \frac{π}{6} + \frac{π}{4})\} = \sin^{- 1} (\cot \frac{π}{2}) = \sin^{- 1} 0 = 0 \end{array}$

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