plz solve this question

If Î¸ and Î± are two real numbers such that
( cos⁴ Î¸/cos² Î±) + (sin⁴ Î¸/sin²Î±) = 1
then prove that: -

(cos²ⁿ⁺² Î¸/cos²ⁿÎ±) + (sin²ⁿ⁺²Î¸/sin²ⁿÎ±) = 1
for integral values of n.

1 Answers

( cos⁴ Î¸/cos²Î±) + (sin⁴ Î¸/sin²Î±) = 1

so,

( cos⁴ Î¸. sin²Î±) + (sin⁴ Î¸. cos²Î±) = cos²Î±. sin²Î±

now u can reduce it to get

(cos²Î¸-cos²Î±)²=0!!

This is done by taking sin²Î± in the numerator in the first step as 1-cos²Î±

Then again at one stage take sin²Î¸ as 1-cos²Î¸

U should be through..

Try or else i will give the whole solution :)

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω