Question

prove sin 47 + cos 77 = cos 17

Answer 1

I hope this answer help you

Answer 2

Answer and Explanation:

To prove : $\sin 47+\cos 77=\cos 17$

Solution :

Taking LHS,

$\sin 47+\cos 77$

$=\sin (90-43)+\cos 77$

We know, $\sin(90-\theta)=\cos \theta$

$=\cos 43+\cos 77$

Apply trigonometry formula,

$\cos A+\cos B=2\cos (\frac{A+B}{2})\cos (\frac{A-B}{2})$

$=2\cos (\frac{43+77}{2})\cos (\frac{43-77}{2})$

$=2\cos (\frac{120}{2})\cos (\frac{-34}{2})$

$=2\cos (60)\cos (-17)$

Applying, $\cos (60)=\frac{1}{2},\ \ \cos(-\theta)=\cos \theta$

$=2\times \frac{1}{2}\cos (17)$

$=\cos (17)$

=RHS

LHS=RHS hence proved.