### Home > PC > Chapter 9 > Lesson 9.2.2 > Problem 9-86

9-86.

**Challenge:**Given*f*(*x*) = tan*x*. Homework Help ✎Use the fact that sin(

*x*+*y*) = sin*x*cos*y*+ cos*x*sin*y*

and cos(*x*+*y*) = cos*x*cos*y*− sin*x*sin*y*to show that

. At this point, can you find

? Explain. Find the resulting equation when multiplying by

. It is known that

. Use this fact and your answer to part (c) to show that when

for f( *x*) = tan*x*is applied, the result is sec^{2}x.

No, you would have division by 0.