Question

Number 19 only! 100 points!

Rewrite each expression in terms of sine and cosine, and simplify as much as possible.

Answer 1

The answer is sin^2

Answer 2

The answer is sin^2 (theta) cos (theta) .

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) .