Solve the equation 1 tan theta sqrt3 2 cos theta 1 0 3 3 t

Solve the equation

1) tan theta = -sqrt3

2) cos theta +1 = 0

3) 3 tan²theta - 1 = 0

please show all steps.

We have given,

tan = - sqrt(3)

Now we know that tan is negative in 2nd and 4th quadrant and the value of tan = sqrt3 is at pi/3

Hence in order to get -sqrt(3) value of = pi- pi/3= 2pi/3

Therefore for tan = -sqrt(3) the general solution is

= 2pi/3 +n*pi for n= 0, 1, 2, 3, ...............

We have given cos +1 = 0

=> cos = -1

Value of cos is -1 at = pi

Hence the genral solution for the given trigonometric equation is

= pi+ 2pi n

3) 3tan^2 -1 =0

=> 3tan^2 = 1

=> tan^2 = 1/3

=> tan = -1/sqrt3 , 1/sqrt3

hence theta = pi/6 +pi n , 5pi/6 + pi n