The value of tan (2tan^-1 ((3)/(5) )+sin^-1 ((5)/(13) ) ) is equal to :

Inverse Trigonometric Functions: The value of tan (2tan^-1 ((3)/(5) )+sin^-1 ((5)/(13) ) ) is equal… | JEE Main 2021

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 1

The value of $\tan\left(2\tan^{-1}\left(\dfrac{3}{5}\right)+\sin^{-1}\left(\dfrac{5}{13}\right)\right)$ is equal to :

Inverse Trigonometric Functions

$\dfrac{-181}{69}$$\dfrac{220}{21}$✓ Correct answer$\dfrac{-291}{76}$$\dfrac{151}{63}$

Solution

$2\tan^{-1}\frac35=\tan^{-1}\frac{15}{8}$ and $\sin^{-1}\frac5{13}=\tan^{-1}\frac5{12}$. Value $=\dfrac{\frac{15}{8}+\frac5{12}}{1-\frac{15}{8}\cdot\frac5{12}}=\dfrac{55/24}{21/96}=\dfrac{220}{21}$. Option (B).

Inverse Trigonometric Functions - JEE Mathematics question (JEE Main 2021 (Online) 20th July Evening Shift)

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