Prove that: (A+B)+ (A-B) (A+B)+ (A-B) = - Vidyadip

Question

Prove that: $\frac{\sin\text{(A+B)}+\sin\text{(A-B)}}{\cos\text{(A+B)}+\cos\text{(A-B)}}=\tan\text{A}$

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Answer

$\text{L.H.S}=\frac{\sin\text{(A+B)}+\sin\text{(A-B)}}{\cos\text{(A+B)}+\cos\text{(A-B)}}$
$=\frac{2\sin\text{A}\cos\text{B}}{2\cos\text{A}\cos\text{B}}$
$=\frac{\sin\text{A}}{\cos\text {A}}$
$=\tan\text{A}$
$\therefore\text{L.H.S}=\text{R.H.S}$
Hence proved.

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