If `tan theta =1/2`, prove that `sin 2theta + 2cos 2theta = 2`

If tan theta=(a)/(b), prove that (a sin theta-b cos theta)/(a sin theta+b cos theta)=(a^(2)-b^(2))/(a^(2)+b^(2))

If tan^4theta - tan^2 theta= 1 , then prove that cos^4theta+ cos^2theta = 1

If tan^4theta+tan^2theta=1 , prove that, cos^4 theta+cos^2theta=1

Prove that: (sin2 theta)/(1+cos2 theta)=tan theta

Prove that: (sin2 theta)/(1+cos2 theta)=tan 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+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

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

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

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