Trignometry doubt

If sin2Î¸+sin2Ï†=12 and cos2Î¸+cos2Ï†=32,
then cos²(Î¸-Ï†) =

a)38
b)58
c)34
d)54

This question is from rd sharma's MCQ.Plz support yur ans with steps.

1 Answers

341

Hari Shankar ·2010-09-06 01:00:29

Two ways:

1) Directly square and add the two expressions to obtain \cos 2(\theta - \phi). Now you can obtain \cos (\theta - \phi)

2) Write the respective equations as

\sin (\theta + \phi) \cos (\theta - \phi) = \frac{1}{4}; \cos (\theta+\phi) \cos (\theta-\phi) = \frac{3}{4}

Now square and add

You should get Option B

√ √ || {} [] () → ~ ^ 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