Go to main content

Prove cos⁴A + sin⁴A = 1 - 1/2(sin²2A)

Can someone please help me to solve this question?

I can't go beyond this:

= cos⁴A + sin⁴A
= (cos2A)2 + (sin2A)2

I can't solve it after this :(

rames asked 2 years ago·

Hi Rames! In this question we need to know:

  • a2 + b2 = (a + b)2 - 2ab or (a - b)2 + 2ab
  • cos2A + sin2A = 1
  • 2sinA.cosA = sin2A

Here is the solution:

= cos⁴A + sin⁴A
= (cos2A)2 + (sin2A)2
= (cos2A + sin2A)2 - 2cos2A.sin2A
= 1 - 222\frac{2^2}{2} sin2A.cos2A
= 1 - 12\frac 12(2sinA.cosA)2
∴ 1 - 12\frac 12sin22A = RHS

Here is the video explanation:

dibas answered 2 years ago