Find exact solutions for the following equations on the inte

Find exact solutions for the following equations on the interval [0 degree, 360 degree). sin^2 theta cos theta = cos theta tan theta + 1 = Squareroot 3 + Squareroot 3 cot theta

Solution

sin^2 theta cos theta= cos theta

sin^2 theta cos theta - cos theta=0

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

cos theta=0 and sin theta=+-1

theta= pi/2, 3pi/2

b. tan theta + 1= sqrt 3 + sqrt 3 cot theta

cot theta=1/tan theta

tan^2 theta + tan theta -sqrt 3 tan theta -sqrt3=0

(tan theta - sqrt3)(tan theta+1)=0

tan theta= sqrt 3   , tan theta=-1

theta=pi/3, 4pi/3 , 3pi/4, 7pi/4