Question

Number 19 only! 100 points!

Answer 1

The answer is sin^2

Answer 2

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) .