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STD 11 - Trigonometrical equations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - Trigonometrical equations4 Marks
MCQ
For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has
  • A
    infinitely many solutions
  • B
    three solutions
  • C
    one solution
  • ✓
    no solution
✓

Answer

Correct option: D.
no solution
d
$\sin x+2 \sin 2 x-\sin 3 x=3 $

$\sin x\left(1+2 \cos x-3+4 \sin ^2 x\right)=3 $

$\left(4 \sin ^2 x+2 \cos x-2\right)=\frac{3}{\sin x} $

$2-4 \cos ^2 x+2 \cos x=\frac{3}{\sin x} $

$\frac{9}{4}-\left(2 \cos x-\frac{1}{2}\right)^2=\frac{3}{\sin x} $

$\text { L.H.S. } \leq \frac{9}{4} \quad \quad \text { R.H.S. } \geq 3$

No solution.

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