Q15 of 268 Page 5

Prove the following identities :

cos4 A + sin4 A + 2 sin2 A. cos2 A = 1

Taking LHS = cos4 A + sin4 A + 2 sin2 A cos2 A

Using the identity,(a + b)2 = (a2 + b2 + 2ab)


Here, a = cos2 A and b = sin2 A


= ( cos2 A + sin2 A) [∵ cos2 θ + sin2 θ = 1]


= 1


More from this chapter

All 268 →
15

Prove the following identities :

(sin θ + cos θ)2 + (sin θ – cos θ)2 = 2

 15

Prove the following identities :

(asin θ + bcos θ)2 + (acos θ – bsin θ)2 = a2 + b2

 15

Prove the following identities :

sin4 A – cos4 A = 2 sin2 A – 1 = 1 – 2 cos2 A = sin2 A – cos2 A

 15

Prove the following identities :

cos4 θ – sin4 θ = cos2 θ – sin2 θ = 2 cos2 θ – 1