QJEEM10Ma543f: JEE Main 2010 Mathematics - Class 11 JEEM10Ma543f Solution: Let cos ⁡ ( α + β ) = 4 5 and sin ( α − β ) = 5 13 , where 0 ≤…

Question

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Let

\cos (α + β) = \frac{4}{5}

and

\sin (α - β) = \frac{5}{13},

where

0 \leq α, β \leq \frac{π}{4} .

Then

t a n 2 α

=

Accepted Answer

\cos (α + β) = \frac{4}{5} \Rightarrow \tan (α + β) = \frac{3}{4}

\sin (α - β) = \frac{5}{13} \Rightarrow \tan (α - β) = \frac{5}{12}

\tan 2 α = \tan [(α + β) + (α - β)]

= \frac{\frac{3}{4} + \frac{5}{12}}{1 - \frac{3}{4} . \frac{5}{12}} = \frac{56}{33}

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