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Need Solution for R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonomeric Functions Exercise 3.14 Question 7 Sub Question 2 Maths Textbook Solution.

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Answer: 0

Given: \cos \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right),|x| \geq 1

Hint: Since \sec ^{-1} x+\operatorname{cosec}^{-1} x=\frac{\pi}{2}applying it.

Solution: We have,

\begin{aligned} &\cos \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right) \\ &=\cos \left(\frac{\pi}{2}\right) \end{aligned}                                                \left[\sec ^{-1} x+\operatorname{cosec}^{-1} x=\frac{\pi}{2}\right]

=0                                                                                            \left[\cos \frac{\pi}{2}=0\right]

Hence, \cos \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)=0

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