Cos ki power 4 Alpha upon cos square theta + sin ki power 4 upon sin squared theta equals to 1 then prove that cos 4 theta upon cos power cos square alpha + sin ki power 4 theta upon sin square alpha equals to 1
Answers
Cos⁴θ /Cos²α + Sin⁴θ/Sin²α = 1 if Cos⁴α /Cos²θ + Sin⁴α/Sin²θ = 1
Step-by-step explanation:
Given
Cos⁴α /Cos²θ + Sin⁴α/Sin²θ = 1
to be proved
Cos⁴θ /Cos²α + Sin⁴θ/Sin²α = 1
Cos⁴α /Cos²θ + Sin⁴α/Sin²θ = 1
=> Cos⁴αSin²θ + Sin⁴αCos²θ = Cos²θSin²θ
=> Cos⁴α(1 - Cos²θ) + (1 - Cos²α)²Cos²θ = Cos²θ(1 - Cos²θ)
=> Cos⁴α - Cos⁴αCos²θ + (1 + Cos⁴α - 2Cos²α)Cos²θ = Cos²θ - Cos⁴θ
=>Cos⁴α - Cos⁴αCos²θ + Cos²θ + Cos⁴αCos²θ - 2Cos²αCos²θ = Cos²θ - Cos⁴θ
=> Cos⁴α - 2Cos²αCos²θ + Cos⁴θ = 0
=> (Cos²α - Cos²θ)² = 0
=> Cos²α - Cos²θ = 0
=> Cos²α = Cos²θ
LHS
Cos⁴θ /Cos²α + Sin⁴θ/Sin²α
= (Cos²α)²/Cos²α + (1 - Cos²θ)²/(1 -Cos²α)
= Cos²α + (1 - Cos²α)²/(1 -Cos²α)
= Cos²α + 1 - Cos²α
= 1
= RHS
QED
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Here is your solution . You will understand very quickly by this method . Please mark me brainliest .
