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Total number of solutions of tan x + cot...

Total number of solutions of tan x + cot x=2cosec x in `[-2pi,2pi]` is equal to

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
`tanx+cotx=2cosecx`
`rArr(sinx)/(cosx)+(cosx)/(sinx)=(2)/(sinx)`
`rArr(1)/(sinx*cosx)=(2)/(sinx)`
`rArrcosx=(1)/(2)rArrx=+-(pi)/(3),+-(4pi)/(3),+-(5pi)/(3)`
Thus ,there are six solutions.
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