CUET · MATHS · PYQ PAPER 2023
If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), then number of solution(s) of the given equation is :
- A One
- B Two
- C Infinite
- D No solution
Answer & Solution
Correct Answer
(A) One
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\) \(\tan ^{-1}\left(\frac{2 x+3 x}{1-(2 x)(3 x)}\right)=\frac{\pi}{4}\) \(\frac{5 x}{1-6 x^{2}}=\tan \left(\frac{\pi}{4}\right)\) \(\frac{5 x}{1-6 x^{2}}=1\) \(5 x=1-6 x^{2}\) \(6 x^{2}+5 x-1=0\) \((6 x-1)(x+1)=0\)…
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