The number of solutions of the equation ^ 3 xcos x + ^ 2 x cos ^ 2 x + ^ 3 xsin x + 1 = 0 in the interval [0, 2π] is equal to

Correct answer: A. 0 The given equation can be written as sin xcos x( ^ 2 x + ^ 2 x) + ^ 2 x ^ 2 x + 1 = 0 Substituting t = sin xcos x in this equation, we get t^ 2 + t + 1 = 0. This equation has no real roots.

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of solutions of the equation ^ 3 xcos x + ^ 2 x cos ^ 2...

The number of solutions of the equation

\sin^{3} xcos x + \sin^{2} x{cos}^{2} x + \cos^{3} xsin x + 1 = 0

in the interval

\left[0, 2\pi\right]

is equal to

Options

A $0$
B $2$
C $4$
D $8$

Correct answer

A. $0$

Step-by-step solution

The given equation can be written as

sin xcos x\left(\sin^{2} x + \cos^{2} x\right) + \sin^{2} x\cos^{2} x + 1 = 0

Substituting

t = sin xcos x

in this equation, we get

t^{2} + t + 1 = 0.

This equation has no real roots.

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