Trigonometry help (IT'S URGENT!)

If (sin(theta)) + (sin(theta))² + (sin(theta))³ = 1, prove that (cos(theta))⁶ - 4 (cos(theta))⁴ + 8 (cos(theta))² = 4.

Guys, I need an answer urgently. TOMORROW IS MY MATHS EXAM(YEAH,I'M GIVING MY ICSE EXAMINATION) AND I NEED HELP URGENTLY!

1 Answers

1357

Manish Shankar ·2014-03-08 22:19:22

sinÎ¸+sin³Î¸=1-sin²Î¸

=> sinÎ¸(1+sin²Î¸)=cos²Î¸

=> sinÎ¸(2-cos²Î¸)=cos²Î¸

Squaring it

=> sin²Î¸(2-cos²Î¸)²=cos⁴Î¸

=> (1-cos²Î¸)(2-cos²Î¸)²=cos⁴Î¸

Simplify it to get the answer

√ √ || {} [] () → ~ ^ 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