Answer:
The answer is sin^2 (theta) cos (theta) .
Step-by-step explanation:
We need to rewrite tan (theta) as sin (theta) /cos (theta)
tan^2 (theta) = sin^2 (theta)/ cos^2 (theta)
We also need to rewrite sec (theta) as 1/ cos(theta)
sec^3 = 1 / cos^3( theta)
tan^2 (theta) sin^2 (theta)
------------------ = ----------------
sec ^3 (theta) cos ^ 2(theta)
---------------------------
1
-----------
cos ^3 (theta)
Remember when dividing fractions, we can use, copy dot flip
sin^2 (theta) cos^3 (theta)
------------------ * -------------------
cos ^ 2(theta) 1
Canceling a cos^2(theta) from the top and bottom,
sin^2 (theta) cos (theta)
------------------ * -------------------
1 1
we are left with
sin^2 (theta) cos (theta)
The answer is sin^2 (theta) cos (theta) .
