Question

prove that: sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta​

Answer 1

Answer:-

To Prove:

Sin² A + Cos⁴ A = Cos² A + Sin⁴ A

We know that,

Sin² A + Cos² A = 1

→ Cos² A = 1 - Sin² A

On squaring both sides we get,

→ (Cos² A)² = (1 - sin² A)²

Using (a - b)² = a² + b² - 2ab in RHS we get,

→ Cos⁴ A = 1² + Sin⁴ A - 2*(1)*(sin² A)

→ Cos⁴ A = 1 + sin⁴ A - 2Sin² A

Putting the value of "Cos⁴ A" we get,

→ Sin² A + 1 + sin⁴ A - 2Sin² A = Cos² A + sin⁴ A

→ 1 - Sin² A + Sin⁴ A = Cos² A + Sin⁴ A

Putting the value of "1 - Sin² A = Cos² A" we get,

→ Cos² A + Sin⁴ A = Cos² A + Sin⁴ A

→ LHS = RHS

Hence, Proved.