Cos^4(θ)/cos^2(α) + sin^4(θ)/ sin^2(α)=1

Question

Prove that cos^4 alpha/cos^ thetha + sin^4alpha/ sin^2thetha= 1

Answer 1

cos⁴ θ / cos² α + sin⁴ θ / sin² α = 1

( cos⁴ θ sin² α + sin⁴ θ cos² α ) / ( sin² α cos² α ) = 1 Multiply both sides by sin² α cos² α

( cos⁴ θ sin² α + sin⁴ θ cos² α ) = sin² α cos² α

cos⁴ α / cos² θ + sin⁴ α / sin² θ = 1

( cos⁴ α sin² θ + sin⁴ α cos² θ ) / ( sin² θ cos² θ ) = 1 Multiply both sides by sin² α cos² α

( cos⁴ α sin² θ + sin⁴ α cos² θ ) = sin² θ cos² θ

This mean this two expressions are equivalent.

So if this two expressions are equivalent,

if cos⁴ θ / cos² α + sin⁴ θ / sin² α = 1

then

cos⁴ α / cos² θ + sin⁴ α / sin² θ is also = 1