trig identities

**ahmedb** · December 7th, 2011, 07:45 PM

how do i proof this:
((2cos(a)-cos^2(a))/(sin^2(a)+cos(a)+1))=1/(1+sec(a))

**Prove It** · December 7th, 2011, 07:53 PM

Originally Posted by ahmedb

how do i proof this:
((2cos(a)-cos^2(a))/(sin^2(a)+cos(a)+1))=1/(1+sec(a))

$\displaystyle \begin{align*} \frac{2\cos{a} - \cos^2{a}}{\sin^2{a} + \cos{a} + 1} &\equiv \frac{\cos{a}\left(2 - \cos{a}\right)}{1 - \cos^2{a} + \cos{a} + 1} \\ &\equiv \frac{\cos{a}\left(2 - \cos{a}\right)}{2 + \cos{a} - \cos^2{a}} \\ &\equiv \frac{\cos{a}\left(2 - \cos{a}\right)}{2 + 2\cos{a} - \cos{a} - \cos^2{a}} \\ &\equiv \frac{\cos{a}\left(2 - \cos{a}\right)}{2\left(1 + \cos{a}\right) - \cos{a}\left(1 + \cos{a}\right)} \\ &\equiv \frac{\cos{a}\left(2 - \cos{a}\right)}{\left(1 + \cos{a}\right)\left(2 - \cos{a}\right)} \\ &\equiv \frac{\cos{a}}{1 + \cos{a}} \\ &\equiv \frac{\cos{a} \left( \frac{1}{\cos{a}} \right) }{ \left( 1 + \cos{a} \right) \left( \frac{1}{\cos{a}} \right) } \\ &\equiv \frac{1}{\frac{1}{\cos{a}} + 1} \\ &\equiv \frac{1}{1 + \sec{a}} \end{align*}$

**ahmedb** · December 7th, 2011, 07:56 PM

is there a program where you got this from?
or is it your brain?

**Prove It** · December 7th, 2011, 07:58 PM

Originally Posted by ahmedb

is there a program where you got this from?
or is it your brain?

My brain, which is better than any computer program

Math Help Forum: trig identities

LinkBack

Thread Tools

Display

trig identities

Re: trig identities

Re: trig identities

Re: trig identities

Similar Math Help Forum Discussions

trig identities

Trig identities

Trig Identities

identities (trig)

Trig identities