Number of solutions of the equation tanx+secx=2cosx in the interval  [0,2π] is

# Number of solutions of the equation $\mathrm{tan}x+\mathrm{sec}x=2\mathrm{cos}x$ in the interval  $\left[0,2\pi \right]$ is

1. A

0

2. B

1

3. C

2

4. D

3

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### Solution:

$⇒2{\mathrm{sin}}^{2}x+\mathrm{sin}x-1=0$

$⇒\left(2\mathrm{sin}x-1\right)\left(\mathrm{sin}x+1\right)=0$$⇒\mathrm{sin}x=\frac{1}{2}$

but

$⇒x=\frac{\pi }{6},\frac{5\pi }{6}$ in $\left[0,2\pi \right]$

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