Question

Prove that cos65°+ cos115=sin155°-sin25°

Answer 1

Step-by-step explanation:

We know that,

$\cos( \frac{\pi}{2} + \alpha ) = - \sin( \alpha )$

So,

$\cos(115) = - \sin(25)$

Eqn(i)

We also know that,

$\sin( \frac{\pi}{2} + \alpha ) = \cos( \alpha )$

So,

$\sin(155) = \cos(65)$

Eqn(ii)

Adding Eqn. (i)+(2i)

Hence, proved