Question

cos⁴ A − sin⁴ A is equal to ______.

(cos⁴ A − sin⁴ A) on simplification, gives

विकल्प

• 2 cos² A + 1

• 2 cos² A − 1

• 2 sin² A − 1

• 2 sin² A + 1

Answer 1

cos⁴ A − sin⁴ A is equal to 2 cos² A − 1.

Explanation:

The given expression is cos⁴ A − sin⁴ A.

Factorising the given expression, we have

cos⁴ A − sin⁴ A = [(cos² A)² − (sin² A)²]

= (cos² A + sin² A) × (cos² A − sin² A) ...[∵ (a² − b²) = (a + b)(a − b)]

= cos² A − sin² A  ...[∵ sin² A + cos² A = 1]

= cos² A − (1 − sin² A) 

= cos² A − 1 + cos² A 

= 2 cos² A − 1