Question

Prove the trigonometric identity cos^4- cos^2= sin^4A-sin^2A

Answer 1

➡ cos⁴ A - cos² A = sin⁴ A - sin² A

➡ LHS = RHS..

➡ LHS = cos⁴ A - cos² A

➡ (cos² A)² - (cos A)²

• cos² θ = 1 - sin² θ

➡ (1 - sin² A) - (cos A)²

➡ 1 + sin⁴ A - 2 sin² A - cos² A

➡ 1 + sin⁴ A - 2 sin² A - (1 - sin² A)

➡ 1 + sin⁴ A - 2 sin² A - 1 + sin² A

➡ sin⁴ A - sin² A = RHS

∴ Hence it is proved...

Step-by-step explanation:

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