Question

cos^4 theta -sin^4 theta +1=2cos^2 theta​

Answer 1

Cos⁴Ø - Sin⁴Ø + 1 = 2Cos²Ø

Taking L.H.S,

Identities used :-

a⁴-b⁴ = (a²-b²)(a²+b²)

1 - Sin²Ø= Cos²Ø

= (Cos²Ø - Sin²Ø)(Cos²Ø+Sin²Ø) + 1

= (Cos²Ø - Sin²Ø) (1) +1

= ( Cos²Ø + 1 - Sin²Ø)

= Cos²Ø + Cos²Ø

= 2Cos²Ø

Hence, Proved...