3. cot x--V3

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Solution

Given that,

cotx=− 3 tanx= 1 cotx = 1 − 3

The value,

tan30°= 1 3

The value of x where tan is negative is,

In the second and fourth quadrant, tan is negative,

Value in the second quadrant is,

180°−30°=150°

And the value in the fourth quadrant is,

360°−30°=330°

So, the principal solutions are,

x=150° x=150× π 180° x= 5π 6

And,

x=330° x=330°× π 180° x= 11π 6

To find the general solution,

Consider,

tanx=tany (1)

tanx= −1 3 (2)

From equations (1) and (2),

tany= −1 3 tany=tan 5π 6 y= 5π 6

General solution is,

x= 5π 6

For x= 5π 6

Thus, the value of x is nπ+ 5π 6 where, n∈z

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