<PRE><B>Question 194509</B>
tan^2a -sin^2a  = sin^2a * tan^2a,,,,let  a  =  theta
,
but  tan =  sin /  cos
,
sin^2 a/cos^2a -sin^2a = sin^2a *tan^2a
,,
remember  cos^2 = sin^2 =1,,,  cos^2a = 1=sin^2a
,
sin^2a / ( 1-sin^2a)  - sin^2a = sin^2a * tan^2a
,
using  lcd = (1-sin^2a)
,
( sin^2a -sin^2a (1-sin^2a) )/ (1-sin^2a) = sin^2a *tan^2a
,
(  sin^2a -sin^2a +sin4a ) (1-sin^2a) = sin^2a * tan^2a
,
but  cos^2a = 1 - sin^2a
,
 sin^4a / cos^2a  =  sin^2a * tan^2a
,
 with  tan =  sin / cos
,
sin^2a * tan^2a = sin^2a * tan^2a</PRE>