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

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The total number of solutions of the equation sin xtan 4x = cos x...

The total number of solutions of the equation sinxtan4x=cosxsin xtan 4x = cos x for all x∈(0,π)x \in \left(0, \pi\right) are

Correct answer

5

Step-by-step solution

\tan 4x = cot x = \tan \left(\dfrac{\pi}{2} - x\right)<br/><br />4x = n\pi + \dfrac{\pi}{2} - x<br/><br />5x = n\pi + \dfrac{\pi}{2} = \left(2n + 1\right)\dfrac{\pi}{2}<br/><br />⇒ x = \left(2n + 1\right)\dfrac{\pi}{10}<br/><br />x = \dfrac{\pi}{10}, \dfrac{3\pi}{10}, \dfrac{5\pi}{10}, \dfrac{7\pi}{10}, \dfrac{9\pi}{10}<br/>Hence,<br />Hence,5solutionsin(0,π)solutions in \left(0, \pi\right)
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