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Sin(A+B)Sin(A-B)

If A,B are ...

Question

If $A, B$ are acute angles, $sin A = \frac{4}{5}, tan B = \frac{5}{12}$ then $sin (A + B) =$

A

\frac{36}{65}

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B

\frac{65}{56}

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C

\frac{65}{63}

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D

\frac{63}{65}

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Solution

The correct option is D $\frac{63}{65}$
REF.Image
$∴ s i n A = 4 / 5, c o s A = 3 / 5$
$s i n B = 5 / 13, c o s B = 12 / 13$
$∴ s i n (A + B) = s i n A c o s B + c o s A s i n B$
$= \frac{4}{5} . \frac{12}{13} + \frac{3}{5} . \frac{5}{13}$
$= \frac{48 + 15}{65} = \frac{63}{65}$
$= (D)$

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