If the inverse trignometric functions take principal values, then cos^-1 ((3)/(10)cos (tan^-1 ((4)/(3) ) )+(2)/(5)sin (tan^-1 ((4)/(3) ) ) ) is equal to :

Inverse Trigonometric Functions: If the inverse trignometric functions take principal values, then… | JEE Main 2022

JEE Main 2022 (Online) 26th June Evening ShiftQuestion 1

If the inverse trignometric functions take principal values, then $\cos^{-1}\left(\frac{3}{10}\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right)+\frac{2}{5}\sin\left(\tan^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to :

Inverse Trigonometric Functions

$0$$\frac{\pi}{4}$$\frac{\pi}{3}$✓ Correct answer$\frac{\pi}{6}$

Solution

$\cos(\tan^{-1}\frac43)=\frac35$, $\sin(\tan^{-1}\frac43)=\frac45$. Argument $=\frac3{10}\cdot\frac35+\frac25\cdot\frac45=\frac{9}{50}+\frac{16}{50}=\frac12$. $\cos^{-1}\frac12=\frac\pi3$. Option (C).

Inverse Trigonometric Functions - JEE Mathematics question (JEE Main 2022 (Online) 26th June Evening Shift)

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