Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is
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 1+sinxcosx=2cosx ⇒1+sinx=2cos2x=2(1−sin2)x ⇒2sin2x+sinx−1=0 ⇒(1+sinx)(2sinx−1)=0 ⇒sinx=−1or12 Now sinx=−1⇒tanx and sec x not defined. Sinx=12⇒x=π6or5π6. ∴The required number of solution is 2.