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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

The general solution of | x| = cos x is (when n ∈ I ) given by

The general solution of \left|\sin x\right| = cos x

is (when

n \in I

) given by

Options

A $n\pi + \dfrac{\pi}{4}$
B $2n\pi \pm \dfrac{\pi}{4}$
C $n\pi \pm \dfrac{\pi}{4}$
D $n\pi - \dfrac{\pi}{4}$

Correct answer

B. $2n\pi \pm \dfrac{\pi}{4}$

Step-by-step solution

Given, \left|\sin x\right| = cos x

<br/><br/>

∴ \sin^{2} x = \cos^{2} x

<br/><br/>

⇒ 2\cos^{2} x = 1

<br/><br/>

⇒ cos x = + \dfrac{1}{\sqrt{2}} [ ∵ cos xcannotbenegative ]

<br/><br/>

⇒ x = 2n\pi \pm \dfrac{\pi}{4}

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