Question

if cos²theta-sin² theta =1/2 find cos⁴ theta-sin⁴ theta​

Answer 1

cos²∅ - sin²∅ = 1/2

we know that ,

cos²∅ + sin²∅ = 1

cos⁴ ∅ - sin⁴ ∅

= (cos²∅)² - (sin²∅)²

= (cos²∅ + sin²∅) (cos²∅ - sin²∅)

= 1*1/2

= 1/2

using formula : x²-y² = (x+y)(x-y)