Answer:
sin 2 ( x ) ⋅ sin 2 ( x ) cos 2 ( x ) → sin 2 ( x ) tan 2 ( x )
Explanation:
Assuming tan = 2 ( x ) − sin 2 ( x ) = tan 2 ( x ) sin 2 ( x ) ,
tart off by rewriting tan 2 ( x ) in to its sin ( x ) and cos ( x ) components.
sin 2 ( x ) cos 2 ( x ) − sin 2 ( x )
Next find a common denominator
(LCD:
cos 2 ( x )⋅ 1 ) sin 2( x ) cos 2 ( x ) ⋅ ( 1 1 ) − sin 2 ( x ) ⋅ cos 2 ( x ) cos 2 ( x ) → sin 2 ( x ) cos 2 ( x ) − sin 2 ( x ) cos 2 ( x ) cos 2 ( x )
Combine in to a single fraction and factor out a
sin 2 ( x) . sin 2 ( x ) − sin 2 ( x ) cos 2 ( x ) cos 2 ( x ) → sin 2 ( x) ⋅ sin 2 ( x ) cos 2 ( x )
Finally just rewrite sin 2 ( x ) ⋅ sin 2 ( x ) cos 2 ( x ) → sin 2 ( x ) tan 2 ( x )