Let (α+β)=(4)/(5) and let (α-β)=(5)/(13) , where 0 ≤ α, β ≤ (π)/(4) , then 2 α=

Correct answer: A. (56)/(33) array ll (α+β)=(4)/(5)& (α+β)=(3)/(4) (α-β)=(5)/(13)& (α-β)=(5)/(12) 2 α= (α+β+α-β)=((3)/(4)+(5)/(12))/(1-(3)/(4) (5)/(12))=(56)/(33) array

JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

Let (α+β)=(4)/(5) and let (α-β)=(5)/(13) , where 0 ≤ α, β ≤ (π)/(4)...

Let

\cos (\alpha+\beta)=\frac{4}{5}

and let

\sin (\alpha-\beta)=\frac{5}{13}

, where

0 \leq \alpha, \beta \leq \frac{\pi}{4}

, then

\tan 2 \alpha=

Options

A $\frac{56}{33}$
B $\frac{19}{12}$
C $\frac{20}{7}$
D $\frac{25}{16}$

Correct answer

A. $\frac{56}{33}$

Step-by-step solution

\begin{array}{ll}\cos (\alpha+\beta)=\frac{4}{5}& \Rightarrow \tan (\alpha+\beta)=\frac{3}{4}\\ \sin (\alpha-\beta)=\frac{5}{13}& \Rightarrow \tan (\alpha-\beta)=\frac{5}{12}\\ \tan 2 \alpha=\tan (\alpha+\beta+\alpha-\beta)=\frac{\frac{3}{4}+\frac{5}{12}}{1-\frac{3}{4} \frac{5}{12}}=\frac{56}{33}\end{array}

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