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AIEEE 2002 Math Solved Paper

Section: Mathematics

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Question : 2 of 74

Marks: +1, -0

The number of solution of

\tan x+\sec x=2 \cos x

[0,2\pi]

2
3
0
1

Solution:

Given equation is

\tan x+\sec x=2 \cos x

\Rightarrow \;\frac{\sin x}{\cos x}+\;\frac{1}{\cos x}=2 \cos x

\Rightarrow \;\frac{\sin x+1}{\cos x}=2 \cos x

\Rightarrow \sin x+1=2 \cos^2 x

\Rightarrow \sin x+1=2(1-\sin^2 x)

\Rightarrow 2 \sin^2 x+\sin x-1=0

\Rightarrow (2 \sin x-1)(1+\sin x)=0

\Rightarrow \sin x=\;\frac{1}{2}

and

\sin x=-1

When

\sin x=\;\frac{1}{2}

then possible

x=30^{\circ}, 150^{\circ}

When

\sin x=-1

then possible

x=270^{\circ}

So three solutions possible.

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