Number of solns. try it(trigno ....)(11 - 1)

VITEEE Preparation › Trignometry questions › Number of solns. try it(trigno ....)(11 - 1)

If x, y \varepsilon ( 0,\pi) and (sin ³ x + sin ⁴ y) + 3 cosec x + 4 cosec y - 9 =0, then no. of solutions of the equation sin x sin y = 12 in ( 0,\pi) is

A) 0 B) 1 C) 2 D) infinite

#Mathematics #Trignometry

UP 0 DOWN 0 0 2
Post on FacebookPost anonymously?

2 Answers

msp ·2010-02-17 18:47:20

by observation x=y=pi/2

UP 0 DOWN 0
Post on FacebookPost anonymously?

341

Hari Shankar ·2010-02-17 19:50:45

Since sin x>0 in the given domain, \sin^3 x + 3 \csc x = \sin^3x + \frac{1}{\sin x}+\frac{1}{\sin x}+\frac{1}{\sin x} \ge 4 (by AM-GM Inequality)

Similarly,

\sin^4 y + 4 \csc y \ge 5

Hence LHS â‰¥0 with equality when sin x = sin y = 1.

Hence sin x sin y = 1/2 has no solutions

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

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

Close [X]

Number of solns. try it(trigno ....)(11 - 1)

2 Answers

Your Answer

Add Image

Similar Questions