Prove the following trigonometrical identities
`tan^2 theta - sin^2 theta = tan^2 theta sin^2 theta`

Prove that : tan^2 theta -sin^2 theta =tan^2 theta sin^2 theta .

Prove that tan^2theta-sin^2theta=tan^2thetasin^2theta .

Solve the following trigonometric equation : tan theta + tan 2 theta + tan 3 theta =0 .

Solve the following trigonometric equation : tan^2 theta+cot^2 theta=2 .

Solve the following trigonometric equation : sin 2 theta + cos theta = 0 .

Solve the following trigonometric equation : tan 2 theta tan 3 theta=1 .

Solve the following trigonometric equation : sin theta + cos theta = sqrt2 .

Solve the following trigonometric equation : tan theta+ cot theta=2 .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Prove the following identity : sec^4 theta- tan^4 theta =1+2 tan^2 theta .