Question

If Cos^4alpha/cos^2beta+sin^4alpha/sin^2beta=1 Then show that cos^4beta/cos^2alpha+sin^4beta/sin^2alpha=? where alpha and beta are complementary angles

Answer 1

Cos⁴β/Cos²α + Sin⁴β/Sin²α = 1  if alpha and beta are complementary angles

Step-by-step explanation:

alpha and beta are complementary angles

as Cosθ = Sin(90 - θ)    & Sinθ = Cos(90 - θ)

=> Cosα = Sinβ    & Cosβ = Sinα

Cos⁴α/Cos²β   + Sin⁴α/Sin²β  = 1

Cos⁴α = Sin⁴β

Cos²β = Sin²α

Sin⁴α = Cos⁴β

Sin²β = Cos²α

Sin⁴β/Sin²α + Cos⁴β/Cos²α = 1

=> Cos⁴β/Cos²α + Sin⁴β/Sin²α = 1

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