Prove that: 47^ + 77^ = 17^ - Vidyadip

Question

Prove that: $\sin47^\circ+\cos77^\circ=\cos17^\circ$

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Answer

We have, $\text{LHS}=\sin47^\circ+\cos77^\circ$ $=\ \sin(90^\circ-43^\circ)+\cos77^\circ$ $=\ \cos43^\circ+\cos77^\circ$ $=\ \cos(60^\circ-17^\circ)+\cos(60^\circ+17^\circ)$ $=\ 2\cos60^\circ\cos17^\circ$ $=\ 2\times\frac{1}{2}\times\cos17^\circ$ $=\ \cos17^\circ$ $=\ \text{RHS}$ $\therefore\ \sin47^\circ+\cos77^\circ=\cos17^\circ\ \text{Hence proved}.$

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