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The number of solution of $\tan x+\sec x=2\cos x$ in $[0,2\pi]$ is

$ (a)\;2\qquad (b)\;3\qquad(c)\;0\qquad(d)\;1$

1 Answer

The given equation is $\tan x+\sec x=2\cos x$
$\Rightarrow \sin x+1=2\cos^2x$
$\Rightarrow \sin x+1=2(1-\sin^2x)$
$\Rightarrow 2\sin^2x+\sin x-1=0$
$\Rightarrow (2\sin x-1)(\sin x+1)=0$
$\Rightarrow \sin x=\large\frac{1}{2}$$-1$
$\Rightarrow x=30^{\circ},150^{\circ},270^{\circ}$
Hence (b) is the correct answer.
answered Oct 4, 2013 by sreemathi.v
edited Jan 8, 2014 by sreemathi.v

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