Help with trigonometry problem!

[Michelle in MO]

My oldest is taking trig/precalculus this year, and is having difficulty with this problem.

The book is Larson & Hostetler Algebra & Trigonometry, 7th Edition (http://www.amazon.com/Algebra-Trigonometry-7th-Ron-Larson/dp/0618643214).

The problem is from the Chapter 7 Review Exercises, p. 582, Problem #17; it's a problem dealing with simplifying trigonometric equations:

cos^2x + cos^2xcot^2x


The answer key at the back of the book says the answer is cot^2x. She keeps getting 1.

It's been so long since I've had trig., and the last math I've done with her was Algebra 2, which was 2 years ago. Can someone help?

[Jane in NC]

My oldest is taking trig/precalculus this year, and is having difficulty with this problem.

The book is Larson & Hostetler Algebra & Trigonometry, 7th Edition (http://www.amazon.com/Algebra-Trigonometry-7th-Ron-Larson/dp/0618643214).

The problem is from the Chapter 7 Review Exercises, p. 582, Problem #17; it's a problem dealing with simplifying trigonometric equations:

cos^2x + cos^2xcot^2x


The answer key at the back of the book says the answer is cot^2x. She keeps getting 1.

It's been so long since I've had trig., and the last math I've done with her was Algebra 2, which was 2 years ago. Can someone help?

Factor the cos^2(x):

cos^2(x)(1 + cot^2(x)) = cos^2(x) (csc^2(x)) ...using a Pythagorean Identity...

= cos^2(x)/sin^2(x) ....relationship of csc x and sin x

= cot^2(x) ....definition of cot x

Assuming here that the 2 is the exponent and x is the argument, yes?

Hope this helps.
Jane

[Michelle in MO]

:grouphug:

Grateful hugs here, Jane!

We sat down together with the book and figured this out. I don't remember anything about sine, cosine, or tangent, but she said that simplifying the problems was supposed to be similar to simplifying an algebraic expression. So, I re-worked the problem using cos^2x = a and cot^2x = b, we got, simply:

ab + a = a(b+1)

Once she saw the term factored out, she was able to solve the rest of the problem.

I've been out of the homeschooling loop too long!

Thank you for your help, Jane! It worked out!