WBJEE · Maths · Trigonometric Ratios & Identities
Let \(\tan \alpha=\frac{a}{a+1}\) and \(\tan \beta=\frac{1}{2 a+1}\) then \(\alpha+\beta\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\pi\)
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…
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