Trigonometry & Inverse Trigonometry
Number of Solutions of arcsin=2arctan
nta_pyq_2023_apr
Grade 12
Question:
For $x\in(-1,1]$, the number of solutions of the equation $\sin^{-1}x=2\tan^{-1}x$ is equal to
Step-by-Step Solution
Key Concept: Use $2\tan^{-1}x=\sin^{-1}\frac{2x}{1+x^2}$ for $|x|\leq1$. Equation becomes $x=\frac{2x}{1+x^2}\Rightarrow x(x^2-1)=0$.
$x=0$ and $x=1$. Number of solutions $=2$.
Correct Answer: 2