Find an acute angle `theta` when `(costheta-sintheta)/(costheta+sintheta)`=`(1-sqrt3)/(1+sqrt3)`

Find an acute angle theta , when (costheta-sintheta)/(costheta+sintheta)=(1-sqrt(3))/(1+sqrt(3))

sqrt(3)costheta+sintheta=2

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

Suppose that costheta=-1/2 and theta is in the 2nd quadrant prove that (4tantheta+4sintheta)/(3costheta-3sintheta)=(4sqrt3)/(3(1+sqrt3))

sintheta+costheta=(sqrt(3)+1)/(2)

sintheta - sqrt(3)costheta =1

solve sqrt3 costheta+sintheta=sqrt2

Write the acute angle theta satisfying sqrt(3)sintheta=costheta .

Prove the following : (All angles are acute angles.) (sintheta+costheta)/(sintheta-costheta)+(sintheta-costheta)/(sintheta+costheta)=2/(sin^(2)theta-cos^(2)theta)