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If log(0.5) sin x=1-log(0.5) cos x, then...

If `log_(0.5) sin x=1-log_(0.5) cos x`, then number of values of `x in [-2pi, 2pi]` is __________.

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, `"log"_(0.5) "sin"x " and log"_(0.5) "cos"x` are defined if `x in (0, pi//2)`
Now,
`"log"_(0.5) "sin" x = 1- "log"_(0.5) "cos"x`
`rArr "log"_(0.5) "sin" x + "log"_(0.5) "cos"x = 1`
`rArr "log"_(0.5) ("sin" x "cos"x) = 1`
`rArr ("sin" x"cos"x) = (0.5)^(1) rArr "sin" 2x = 1 rArr x = (pi)/(4), -(3pi)/(4)`
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OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
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