Hi, I just learn about Pythagorean identities.
As i know that cos^2θ + sin^2θ = 1
but what is the work out to get 1? and why 1?
Thanks.
Consider a right triangle like here, i.e., the hypothenuse is denoted by h, opposite side is a and adjacent side is b.
Then:
sinθ=a/h
cosθ=b/h
and you know from Pythagorean theorem that $\displaystyle a^2+b^2=h^2$.
So if you calculate $\displaystyle cos^2\theta+\sin^2\theta$, you get
$\displaystyle cos^2\theta+\sin^2\theta=\frac{a^2}{h^2}+\frac{b^2 }{h^2}=\frac{a^2+b^2}{h^2}=\frac{h^2}{h^2}=1.$
You can even simplify this by rescaling the triangle so that h=1. (In case you're familiar with unit circle definitions of trigonometric functions, you should know, what I mean.)
BTW you have a whole article about this identity at wikipedia.