Prove that `(1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)`

Solve the equation (1-tantheta)(1+sin2theta)=1+tantheta

Prove that, (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove that: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove the following identities : (1+tan^(2)theta)/(1+cot^(2)theta)=((1-tantheta)/(1-cottheta))^(2)

(i) The points (-1, 0), (4, -2) and (cos 2theta, sin 2 theta) are collinear (ii) The points (-1,0), (4, -2) and ((1-tan^(2)theta)/(1+tan^(2)theta),(2tan theta)/(1+tan^(2)theta)) are collinear

Given cot theta =(7)/(8) , then evaluate (i) ((1+sin theta )( 1-sin theta ))/( (1+cos theta )(1-cos theta )) " "(ii) ((1+sin theta ))/( cos theta )

For which value of an acute angle theta ,(i) ( cos theta )/( 1-sin theta ) +(cos theta )/( 1+sin theta ) =4 is true ? For which value of 0^(@) le theta le 90 ^(@) , above equation is not defined?

Show that (1)/( cos theta ) -cos theta =tan theta .sin theta

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

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