Prove the following trigonometrical identities
`(sinthetatantheta)/(1-costheta) = 1 + sectheta`

Solve the following trigonometric equation : sin theta=-1 .

Prove the following identity : (sin theta tan theta)/ (1-cos theta)=1+ sec theta .

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

Solve the following trigonometric equation : sin theta + cos theta = 1 .

Solve the following trigonometric equation : cos theta -sin theta=-1 .

Prove the following identity : 1/(sec theta+tan theta)= (1-sin theta)/(cos theta) = sec theta-tan theta .

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Prove the following identity : 1/(sec theta+tan theta) -1/(cos theta) = 1/(cos theta) - 1/(sec theta-tan theta) .

Solve the following trigonometric equation : cos theta =1/2 .

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