tan theta=(1)/(2),sin20+2cos2 theta=2

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

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

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

Prove that : (1+sin 2 theta-cos 2 theta)/(1+sin 2 theta+ cos 2 theta)= tan theta .

If A=[[1,tan theta-tan theta,1]], show that A'A^(-1)=[[cos2 theta,-sin2 thetasin2 theta,cos2 theta]]

Prove: (tan theta+(1)/(cos theta))^(2)+(tan theta-(1)/(cos theta))^(2)=2((1+sin^(2)theta)/(1-sin^(2)theta))

Prove that (sin theta+cos theta)/(sin theta- cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = ( 2sec^(2) theta)/(tan^(2) theta -1) .

Prove that (1+tan theta)/(1-tan theta) = (1 - sin 2 theta)/(cos 2 theta) .

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .

Show that (sin^2 theta)/(1-cot theta)+(cos^2 theta)/(1-tan theta )=1+sin theta cos theta