Question

prove that cos power 4 minus sin power 4 theta is equal to cos 2a​

Answer 1

Answer:

LHS=cos⁴θ-sin⁴θ

= (cos²θ)²-(sin²θ)²

= (cos²θ+sin²θ)(cos²θ-sin²θ)

= cos²θ-sin²θ

= cosθcosθ - sinθsinθ

= cos(θ+θ)

= cos2θ   =  RHS

HENCE PROVED

There is an identity used in this,

cos(A+B) = cosAcosB - sinAsinB

But in this case, A+B, so identity becomes,

cos2A=cos²A-sin²A