Question

cos 52 degree + cos 68 degree + cos 172 degree=

Answer 1

first of all cos 172 = -cos 8
So now we have
= cos 52 + cos 68 - cos 8

Applying Identity,
cos A − cos B = −2 sin ½ (A + B) sin ½ (A − B)

let's look at our cos 52 - cos8,
here let's A = 52, B=8
cos 52 - cos 8 = -2sin[60/2]sin[44/2]
cos52 -cos8 = - sin 22
so
cos 52 + cos 68 + cos172
= cos52 + cos68 - cos8
= cos52 - cos8 + cos68
= - sin22 + cos68
but by the complementary relationship
sin 22 = cos68 , (since 22+68 = 90)
so finally
= -cos 68 + cos 68
= 0

Answer 2

find ur ans attached....