Q3 of 62 Page 81

Prove that -

(cos x + cos y)2 + (sin x - sin y)2 = 4 cos2[(x + y)/2]

We know that-




L.H.S = (cos x + cos y)2 + (sin x - sin y)2





= 4 cos2[(x + y)/2]×1 [∵ sin2x + cos2x = 1]


= 4 cos2[(x + y)/2]


= R.H.S


Hence, L.H.S = R.H.S…Proved


More from this chapter

All 62 →
1

Prove that

2

Prove that (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

 4

Prove that -

(cos x - cos y)2 + (sin x - sin y)2 = 4 sin2[(x-y)/2]

 5

Prove that-

sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x