JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

The number of the solutions of the equation

\sin 5 x \cos 3 x

=\sin 6 x \cos 2 x

in the interval

[0, \pi]

, is

View answer and explanation

Correct option: C

The correct answer is 5 because there are 5 solutions to the given equation within the specified interval [0,

\pi

], found by simplifying the equation and solving for x.

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\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x

\left[ {0,\;\,\frac{\pi }{2}} \right]

\left( {x,\,y} \right)

x,\,\,y \in \left[ {0,10} \right]

\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

\mathrm{X}

\theta \rightarrow \frac{\pi}{2}

\sin x+\cos x=\frac{\sqrt{7}}{2}

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0 < x < \pi

\cos x+\sin x=\frac{1}{2}

\tan x