How do I prove this trigonometric identity?

Algebra
Tutor: None Selected Time limit: 1 Day

Aug 9th, 2015

Thank you for the opportunity to help you with your question!

First recognize that cotx = cosx / sinx

then,

cot^2x + cotx / cot^2x - 1 = (cos^2x/sin^2x + cosx/sinx) / (cos^2x/sin^2x - 1)

Multiply numerator and denominator by sin^2x to eliminate sin^2x in the fractions, to get

(cos^2x + sinxcosx) / (cos^2x - sin^2x)  notice the perfect square in the denominator

factor numerator and denominator:

cosx(cosx + sinx) / (cosx + sinx)(cosx - sinx)

= cosx / cosx - sinx

Now go back to the original equation with the 1 and the 3 and substitute the cot^2 fraction with cosx / cosx - sinx :

1 - cosx / cosx - sinx + 3    Now use common denominator cosx - sinx and substitute for 1 and 3 :

(cosx - sinx / cosx - sinx) - (cosx / cosx - sinx) + (3cosx - 3sinx / cosx - sinx)   Now combine and simplify to get

3cosx - 4 sinx / cosx - sinx

Done





Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 9th, 2015

Thank you so much, all I needed was the perfect square. I'll have to rememebr that for the future.

Aug 9th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Aug 9th, 2015
...
Aug 9th, 2015
Feb 25th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer