Question

If (cos⁴ α/cos² β) + (sin⁴ α/sin² β) = 1, prove that 

(i) sin⁴ α + sin⁴ β = 2 sin² α sin² β 

(ii) (cos⁴ β/cos² α) + (sin⁴ β/sin² α) = 1

Answer 1

(i) Given (cos⁴ α/cos² β) + (sin⁴ α/sin² β) = 1

(ii) (cos⁴ β/cos² α) + (sin⁴ β/sin² α) = 1