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Evaluate: `Cot(Sin^-1 3/4+Sec^-1 4/3)`

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Question

Evaluate: 

`cot(sin^-1  3/4+sec^-1  4/3)`

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Solution

`cot(sin^-1  3/4+sec^-1  4/3)`

`=cot(sin^-1  3/4 + cos^-1  3/4)`     `[thereforesec^-1x=cos^-1  1/x]`

`=cot(pi/2)`     `[thereforesin^-1x+cos^-1x=pi/2]`

= 0

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Chapter 3: Inverse Trigonometric Functions - Exercise 4.10 [Page 66]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 3 Inverse Trigonometric Functions
Exercise 4.10 | Q 1.1 | Page 66
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