SOLUTION: prove this trig identity (5 marks): tanx-1 = (sin^2x-cos^2x)/(sinxcosx+cos^2x) I've wasted a good 8 pages trying to work this out haha. thanks in advance!

Algebra ->  Trigonometry-basics -> SOLUTION: prove this trig identity (5 marks): tanx-1 = (sin^2x-cos^2x)/(sinxcosx+cos^2x) I've wasted a good 8 pages trying to work this out haha. thanks in advance!      Log On


   

Question 199537: prove this trig identity (5 marks):
tanx-1 = (sin^2x-cos^2x)/(sinxcosx+cos^2x)
I've wasted a good 8 pages trying to work this out haha. thanks in advance!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation.


... Factor the numerator using the difference of squares formula

... Factor out the GCF cos%28x%29 from the denominator


... Cancel out the common terms.


... Break up the fraction.


... Replace sin%28x%29%2Fcos%28x%29 with tan%28x%29


... Reduce cos%28x%29%2Fcos%28x%29 to get 1


So this verifies the identity.