Factoring trigonometric equation

[sapiental]

Hi,

I'm having trouble understanding how my math book factored the following equation.

[(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))]

to get

[(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))]

I get the numerator but I don't understand what happened to the cosine in the denominator..

Any suggestions?

Thanks

 

[Hurkyl]

I don't believe those are equal. For example, if you plug in t=0, the first expression is equal to -1, and the second is +1. Presumably it's just a typo.

Anyways, this is why you studied trig identities in precalc. Pretend you were given the following problem.


Prove the identity:

(cos t)(cos t) - (1 + sin t)(sin t) = (1 + sin t)(1 - 2 sin t)​

 

[sapiental]

oh right

cos^2(x) + sin^2(x) = 1

thanks!