Find the soln...trigo series

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(1 + tan5Â°) (1 + tan10Â°) (1 + tan15Â°).........( 1 + tan45Â°) = 2^k ,

then k equals ___

then answer is an integer (0 - 9)

#Mathematics #Trignometry

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2 Answers

Lokesh Verma ·2011-05-11 01:40:10

Hint:

(1 + tan AÂ°)(1 + tan (45Â°-A)) =

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aditya ravichandran ·2011-05-11 01:52:05

\tan(A-B)=\frac{\tan{A}-\tan{B}}{1+\tan{A}\tan{B}}\\ \text{Put A=pi/4;B=x} \\ (1+\tan(\frac{\pi}{4}-x)-1)=\frac{1-\tan{x}}{1+\tan{x}}\\ \boxed{(1+\tan(\frac{\pi}{4}-x))(1+\tan{x})=2}\\ \text{so we can club the conjugates i.e 5,40;10,35;15,30;20;25}\\ \texttt{Answer:5}

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ 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

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Find the soln...trigo series

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