Question

iv) sin 23° + sin 37° = cos7​

Answer 1

SOLUTION

L.H.S

=) sin23° + sin37°

$= > (sin \: A+ sin \:B= 2sin \frac{A+ B}{2} cos \frac{A- B}{2}) \\ = > 2sin \: \frac{23 \degree + 37 \degree}{2} cos \frac{23 \degree - 37 \degree}{2} \\ \\ = > 2sin \frac{60 \degree}{2} cos \frac{ - 1 4 \degree}{2} \\ \\ = > 2sin \frac{60 \degree}{2} cos \frac{ - 14 \degree}{2} \\ = > 2sin30 \degree \: \: cos - 7 \degree \\ = > {cos( - A) = cos A} \\ = > 2 \times \frac{1}{2} \times cos7 \degree \\ \\ = > cos 7 \degree$

R.H.S.

Hence proved

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