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Question

Number of solutions of the equations tan x + sec x=2 cos x lying in the interval [0,2π]

A
1
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B
2
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C
3
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Solution

The correct option is B 2
The given equation can be written as sin x+1cos x=2 cos xsin x+1=2 cos2x(cos x0)2 sin2x+sin x1=0(2 sin x1)(2 sin x+1)=0sin x=12(sin x+10 as cos x0)x=π6,5π6in[0,2π]. The required number of solutions is 2.

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