Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minPYQ_2017

MathematicsMediumsingle choice

The general solution of $\sin x - 3 \sin 2 x + \sin 3 x = \cos x - 3 \cos 2 x + \cos 3 x$ is

Answer:

Solution:

We have,

$\sin x - 3 \sin 2 x + \sin 3 x = \cos x - 3 \cos 2 x + \cos 3 x$

$\Rightarrow \sin x + \sin 3 x - 3 \sin 2 x = \cos x + \cos 3 x - 3 \cos 2 x$

$\Rightarrow 2 \sin 2 x \cos x - 3 \sin 2 x - 2 \cos 2 x \cos x + 3 \cos 2 x = 0$

$\Rightarrow \sin 2 x (2 \cos x - 3) - \cos 2 x (2 \cos x - 3) = 0$

$\Rightarrow (\sin 2 x - \cos 2 x) (2 \cos x - 3) = 0$

$\Rightarrow \sin 2 x = \cos 2 x [∵ \cos x \neq 3 / 2]$

$\Rightarrow 2 x = 2 n π \pm (\frac{π}{2} - 2 x)$

$\Rightarrow x = \frac{n π}{2} + \frac{π}{8}$ [ $∵$ neglect $- ve$ sign]

Stream:BITSATSubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2017

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