Find all values of theta where 0 lessthanorequalto theta les

Find all values of theta where 0 lessthanorequalto theta lessthanorequalto 360 degree that satisfy the given equation 4 tan theta - sec^2 theta = 0.

Solution

4 tan theta - sec^2 theta = 0

tan theta = sin theta / cos theta

sec theta = 1/ cos theta

therefore we can write

4 ( sin theta /cos theta ) - ( 1 / cos^2 theta ) = 0

( -1 + 4 cos theta sin theta )/ cos^2 theta = 0

or

-1 + 4 cos theta sin theta = 0

sin 2 theta = 1/2

2 theta = pi/6 + 2pin

2 theta = 5pi/6 + 2pin

theta = 5pi/12 , 17pi/12,13pi/12, pi/12