Question

Prove that sin⁴∅+cos⁴∅=1-2sin²∅cos²∅

Answer 1

Answer:

(a+b)² = a²+b²+2ab

a²+b² = (a+b)² - 2ab -------( eq 1 )

given:-

LHS = sin⁴∅+cos⁴∅

= (sin²∅)² + (cos²∅)²

= (sin²∅ + cos²∅)² - 2sin²∅cos²∅ (same as eq 1)

= 1² - 2sin²∅cos²∅ (since sin²∅+cos²∅=1)

= 1 - 2sin²∅cos²∅ = RHS

Hence proved