Solve `sin^2 theta tan theta+cos^2 theta cot theta-sin 2 theta=1+tan theta+cot theta`

(sin theta+cos theta)(tan theta+cot theta)=

If tan theta+cot theta=2 then sin theta+cos theta=

Prove that sin theta(1+tan theta)+cos theta(1+cot theta)=sec theta+cos ec theta

cos ect theta(sec theta-1)-cot theta(1-cos theta)=tan theta-sin theta

(cos ec theta-sin theta)(sec theta-cos theta)(tan theta+cot theta)=1

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

Prove that: (a) (sin 2 theta)/(1+cos 2 theta)=tan theta (b) (1+sin 2 theta+cos 2theta)/(1+sin2 theta-cos 2 theta)=cot theta