precalculus identities

aggy113 · #1 Sep 24, 2009, 03:30 PM

prove the following identities?
a.) (1 - cosX)(cscX + cotX)=sinX

ArcSine · Sep 25, 2009, 03:04 AM

Here's one way your proof could proceed: Working on the left-hand side, multiply it out:

$csc\theta + cot\theta - cos\theta csc\theta - cos\theta cot\theta$

Re-express the terms (I'll let you fill in the steps in your proof):

$\frac{1}{sin\theta}\ +\ \frac{cos\theta}{sin\theta} \ - \ \frac{cos\theta}{sin\theta} \ - \ \frac{cos^2 \theta}{sin\theta}$

Note that two of the terms cancel out, and the remaining two terms, having a common denominator, can be written

$\frac{1-cos^2 \theta}{sin\theta}$

Now look at the numerator, and think of the Pythagorean Identity. Can you finish it up from here?

Also keep in mind that with many trig IDs there are multiple possible paths to the same conclusion. Good luck!



At Ask Me Help Desk you can ask questions in any topic and have them answered for free by our experts. To ask questions or participate in answering them you must register for a free account. By registering you will be able to: Get free answers from experts in any of our 300+ topics. Accept money for answers that you provide. Communicate privately with other members (PM). See fewer ads. Sign Up!