Question

cos55+cos65+cos175=0

Answer 1

hence proved ...i think u got it...

Answer 2

Answer and explanation:

To prove : $\cos 55+\cos 65+\cos 175=0$

Solution :

Taking LHS,

$LHS=\cos 55+\cos 65+\cos 175$

Applying trigonometric identity,

$\cos a+\cos b=2\cos (\frac{a+b}{2}) \cos (\frac{a-b}{2})$

$LHS=2\cos (\frac{55+65}{2}) \cos (\frac{55-65}{2})+\cos 175$

$LHS=2\cos (\frac{120}{2}) \cos (\frac{-10}{2})+\cos 175$

$LHS=2\cos (60) \cos (-5)+\cos 175$

$LHS=2\times\frac{1}{2}\cos (-5)+\cos 175$

$LHS=\cos 5+\cos (180-5)$

As $\cos (180-x)=-\cos x$

$LHS=\cos 5-\cos 5$

$LHS=0$

$LHS=RHS$

Hence proved.