##### How do I prove this trigonometric identity?

 Algebra Tutor: None Selected Time limit: 1 Day

Aug 9th, 2015

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

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

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Aug 9th, 2015
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Aug 9th, 2015
May 28th, 2017
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