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Solving Trigonometric Equations
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Qn #1834
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00:00
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The equation $\sin^4 x + \cos^4 x + \sin 2x + \alpha = 0$ is solvable for:
A.
$-\dfrac{1}{2} \le \alpha \le \dfrac{1}{2}$
B.
$-3 \le \alpha \le 1$
C.
$-\dfrac{3}{2} \le \alpha \le \dfrac{1}{2}$
D.
$-1 \le \alpha \le 1$
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Qn #1820
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If $\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$ then $x$ satisfies the equation:
A.
$2x^2 - x + 2 = 0$
B.
$2x^2 - 3x = 0$
C.
$2x^2 + x - 1 = 0$
D.
None of these
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Qn #1718
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The general solution of $ \sqrt{3}\cos x + \sin x = 3 $ is:
A.
$2n\pi \pm \dfrac{\pi}{6}$
B.
$2n\pi \pm \dfrac{\pi}{3}$
C.
No solution
D.
$n\pi \pm \dfrac{\pi}{6}$
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Qn #1428
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If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is
A.
$\frac{4-\sqrt{7}}{3}$
B.
$\frac{4+\sqrt{7}}{3}$
C.
$\frac{1+\sqrt{7}}{4}$
D.
$\frac{1-\sqrt{7}}{4}$
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Qn #1248
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The value of A that satisfies the equation asinA + bcosA = c is equal to
A.
$\tan^{-1}\left(\dfrac{a}{b}\right) \pm \cos^{-1}\left(\dfrac{c}{\sqrt{a^2 + b^2}}\right)$
B.
$\tan^{-1}\left(\dfrac{c}{b}\right) \pm \cos^{-1}\left(\dfrac{a}{\sqrt{a^2 + b^2}}\right)$
C.
$\tan^{-1}\left(\dfrac{a}{b}\right) \pm \sin^{-1}\left(\dfrac{c}{\sqrt{a^2 + b^2}}\right)$
D.
None of these
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Qn #1168
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The number of solutions of the equation
sinx + sin5x = sin3x
lying in the interval $[0, \pi]$ is
A.
4
B.
6
C.
5
D.
2
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Solving Trigonometric Equations Practice Questions | Group Studies Library | Tancet Group Studies