Show that :

`( 1 - Cos^2( theta ) ) / Sin^2( theta )` = 1

Show : 1 - Sin^4theta = Cos^2theta ( 1 + Sin^2theta )

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

If 3 cot theta= 2 , show that ((4 sin theta - 3 cos theta ))/((2 sin theta + 6 cos theta))=(1)/(3)

Show that (cos^(2)theta - sin^(2)theta)=(2tan theta)/((1- tan^(2)theta)) is not an identity .

Show that : (1+ tan theta/2)/(1-tan theta/2) = (1+sin theta)/(cos theta) = tan (pi/4 + theta/2)

1- (sin ^ (2) theta) / (1 + cos theta) + (1 + cos theta) / (sin theta) - (sin theta) / (1-cos theta) - (1) / (sec theta)

Show that :((cos theta-cos3 theta)(sin8 theta+sin2 theta))/((sin5 theta-sin theta)(cos4 theta-cos6 theta))=1