$sin 47^{o} + cos 77^{o} = cos 17^{o}$

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Solution

Simplifying the LHS of $sin 47^{\circ} + cos 77^{\circ} = cos 17^{\circ}$ .

$sin 47^{\circ} + cos 77^{\circ} = sin (90^{\circ} - 43^{\circ}) + cos 77^{\circ}$

$= cos 43^{\circ} + cos 77^{\circ}$

$= 2 cos \frac{43^{\circ} + 77^{\circ}}{2} cos \frac{43^{\circ} - 77^{\circ}}{2}$

$= 2 cos 60^{\circ} cos 17^{\circ}$

$= 2 \times \frac{1}{2} cos 17^{\circ}$

$= cos 17^{\circ}$

$= R H S$

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