Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsIdentities, eqations and inequations involving ITFMedium2 minPYQ_2023

MathematicsMediumnumerical

For $x \in (- 1, 1]$ , the number of solutions of the equation $\sin^{- 1} x = 2 \tan^{- 1} x$ is equal to

Answer:

2.00

Solution:

Given that $\sin^{- 1} x = 2 \tan^{- 1} x$
$\Rightarrow \sin^{- 1} x = \sin^{- 1} (\frac{2 x}{1 + x^{2}})$
$\Rightarrow x = (\frac{2 x}{1 + x^{2}})$
$\Rightarrow x + x^{3} = 2 x$
$\Rightarrow x^{3} - x = 0$
$\Rightarrow x (x^{2} - 1) = 0$
$\Rightarrow x = 0, - 1, 1$ .
But $x \in (- 1, 1]$ , so the number of roots are $2$ , $x = 0 & 1$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Identities, eqations and inequations involving ITF

⏱ 2mℹ️ Source: PYQ_2023

Doubts & Discussion

Loading discussions...