Question

Prove that:
2(Sin⁶A+Cos⁶ A)- 3(Sin⁴ A +Cos⁴ A)+1
= 0​

Answer 1

Step-by-step explanation:

LHS

= 2 ( sin⁶ + cos⁶ ) - 3 ( sin⁴ + cos⁴ ) + 1

= 2 [( sin² + cos² )³ - 3 sin² cos²( sin² + cos² )] - 3 [( sin² + cos² )² - 2 sin² cos²] + 1

= 2 [ (1)³ - 3 sin² cos² (1) ] - 3 [ (1)² - 2 sin² cos² ] + 1

= 2 - 6 sin² cos² - 3 + 6 sin² cos² + 1

= 0

HENCE PROVED