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WBJEE · Maths · Trigonometric Ratios & Identities

Let \(\tan \alpha=\frac{a}{a+1}\) and \(\tan \beta=\frac{1}{2 a+1}\) then \(\alpha+\beta\) is

  1. A \(\frac{\pi}{4}\)
  2. B \(\frac{\pi}{3}\)
  3. C \(\frac{\pi}{2}\)
  4. D \(\pi\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi}{4}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Hints: } \tan \alpha=\frac{a}{a+1}, \tan \beta=\frac{1}{2 a+1} \\ & \tan (\alpha+\beta)=\frac{\frac{a}{a+1}+\frac{1}{2 a+1}}{1-\frac{a}{(a+1)(2 a+1)}}=\frac{\frac{a(2 a+1)+a+1}{(a+1)(2 a+1)}}{\frac{(a+1)(2 a+1)-a}{(a+1)(2 a+1)}}=\frac{2 a^2+2 a+1}{2…