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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - Trigonometrical equations1 Mark
MCQ
The equation $\sqrt 3 \sin x + \cos x = 4$ has
  • A
    Only one solution
  • B
    Two solutions
  • C
    Infinitely many solutions
  • ✓
    No solution
✓

Answer

Correct option: D.
No solution
d
(d) Given equation is $\sqrt 3 \sin x + \cos x = 4$

which is of the form $a\sin x + b\cos x = c$ with $a = \sqrt 3 ,\,b = 1,\,c = 4$.

Here ${a^2} + {b^2} = 3 + 1 = 4 < {c^2},$

therefore the given equation has no solution.

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