JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1

\tan \alpha=\left(1+2^{-x}\right)^{-1}, \tan \beta=\left(1+2^{x+1}\right)^{-1}

, then

\alpha+\beta

equals

View answer and explanation

Correct option: B

\pi / 4

Option B (

\frac{{\pi}}{{4}}

) is correct because by substituting

t = 2^x

and using the tangent addition formula,

\tan(\alpha + \beta)

simplifies to 1, which means

\alpha + \beta = \frac{{\pi}}{{4}}

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