Question

Verify the identity.

Answer 1

Where is it?

Answer 2

\[\left(\begin{matrix}1-\sin(x) \\ \cos (x)\end{matrix}\right)= \left(\begin{matrix}\cos(x) \\ 1+\sin(x)\end{matrix}\right)\]

Answer 3

I haven't even done anything yet... hang on...

Answer 4

Ok, start with the pythagorean identity, I guess
\[\huge \cos^2 x + \sin^2 x = 1\]

Answer 5

if u doing from left side : 1-sin(x) / cos(x)
multiply that fraction by 1+sin(x) / 1+sin(x)
what u get ?

Answer 6

and put the sin part on the other side
\[\huge \cos^2 x = 1 - \sin^2 x\]

Answer 7

You know difference of two squares, right?
\[\huge (\cos x)(\cos x) = (1-\sin x)(1+\sin x)\]

Answer 8

and so you can divide both sides by cos x
\[\huge \cos x = \frac{(1-\sin x)(1+\sin x)}{\cos x}\]
And then divide both sides by 1+sin x
\[\huge \frac{\cos x}{1+\sin x} = \frac{1-\sin x}{\cos x}\]

Answer 9

And you're done.

Answer 10

ok thanks :)

Answer 11

No problem :)