NDA 2016 Maths · Mathematics · Trigonometric Equations · medium

The number of solutions of sin x+cos x=1 in the interval [0,2π) is

Single correct option

The number of solutions of

\sin x+\cos x=1

in the interval

[0,2\pi)

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Answer: (A) $2$

Rewrite as

\sqrt2\sin\left(x+\dfrac\pi4\right)=1

, so

\sin\left(x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

. Then

x+\dfrac\pi4=\dfrac\pi4

\dfrac{3\pi}4

, giving

x=0

and

x=\dfrac\pi2

. Squaring the equation would introduce an extra root

x=\pi

, which fails the original equation.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake