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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 cot xcos x - 1 = cot x -...

The number of solutions of the equation $cot xcos x - 1 = cot x - cos x, \forall x \in \left[0, 2\pi\right] is equal to

Correct answer

2

Step-by-step solution

cot⁡x⋅cos⁡x−cot⁡x+(cos⁡x−1)=0\cot x ⋅ \cos x - \cot x + \left(\cos x - 1\right) = 0
⇒(cotx+1)(cosx−1)=0⇒ \left(cot x + 1\right)\left(cos x - 1\right) = 0
⇒cotx=−1orcosx=1⇒ cot x = - 1 or cos x = 1 (Not possible as sinx≠0sin x \ne 0)
Hence, 22 solutions are possible in \left[0, 2\pi\right]
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