#### Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.10 Question 1 Subquestion (i) Maths Textbook Solution.

Answer: $0$
Hint: Check if there is any relation between$\sec ^{-1}x$  and $\cos^{-1}x$ . Use inverse trigonometric functions properties to solve. $( \therefore \sec^{-1}x = \cos^{-1}\frac{1}{x} )$
Given:$\cot\left (\sin^{-1}\frac{3}{4}+ \sec^{-1}\frac{4}{3} \right )$
Solution: Let replace$\sec^{-1}\frac{4}{3}$  by $\cos^{-1}\frac{3}{4}$   because
$\therefore \sec^{-1}x = \cos^{-1}\frac{1}{x}$
$= \cos^{-1}\frac{3}{4}$
Now, $\Rightarrow \cot\left (\sin^{-1}\frac{3}{4}+ \sec^{-1}\frac{4}{3} \right )$
Again by property,$\sin^{-1}x+ \cos^{-1}x= \frac{\pi }{2}$
Now $\Rightarrow \cot\left (\sin^{-1}\frac{3}{4}+ \cos^{-1}\frac{3}{4} \right )$
$\! \! \! \! \! \! \! \! \! \Rightarrow \cot\frac{\pi }{2}\\ = 0 \; \; \; \; \; \; [\because \cot\frac{\pi }{2}=0]$
Hence, $\cot\left (\sin^{-1}\frac{3}{4}+ \sec^{-1}\frac{4}{3} \right )= 0$
Concept: Properties and relations between inverse trigonometric functions.
Note: Inverse trigonometric functions remember relation between all trigonometric functions. Also, try to remember value of trigonometric functions.