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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 tan x + sec x = 2cos x...

The number of solutions of the equation tanx+secx=2cosxtan x + sec x = 2cos x lying in the interval [0,5π]\left[0,5\pi\right] is

Correct answer

6

Step-by-step solution

tanx+secx=2cosxtan x + sec x = 2cos x
⇒sinx+1=2cos⁡2x=2−2sin⁡2x⇒ sin x + 1 = 2\cos^{2} x = 2 - 2\sin^{2} x
⇒2sin⁡2x+sinx−1=0⇒ 2\sin^{2} x + sin x - 1 = 0
⇒sinx=12,−1⇒ sin x = \dfrac{1}{2}, - 1
sinx=−1⇒cosx=0sin x = - 1 ⇒ cos x = 0 and hence tanx,secxtan x, sec x is not defined
So, sinx=12sin x = \dfrac{1}{2}

Hence, in [0,5π]\left[0,5\pi\right] there are 66 solutions.

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