
Prove this identity
I'm not sure how to prove these expressions true...the question is:
Prove that each expression is an identity for all values for which it is defined.
$\displaystyle
\frac {sin\theta} {sin\theta+cos\theta} = \frac {tan\theta} {1+tan\theta}
$
and,
$\displaystyle
\frac {sin^2\theta+2cos\theta1} {sin^2+3cos\theta3} = \frac {1} {1sec\theta}
$
Thank you! :D

$\displaystyle \dfrac{\sin x}{\sin x+\cos x}$
divide the numerator and denominator by cosx
$\displaystyle \dfrac{\frac{\sin x}{\cos x}}{\frac{\sin x+\cos x}{\cos x}}$
For the other question, show some effort. Where exactly are you stuck?

Oh, wow, that was so obvious hahaha
Thanks!! :D
Any ideas on the second one?

$\displaystyle \dfrac{\sin^2 x+2\cos x1}{\sin^2 x+3\cos x3}$
$\displaystyle = \dfrac{1\cos^2 x+2\cos x1}{1\cos^2 x+3\cos x3}$
$\displaystyle = \dfrac{\cos^2 x+2\cos x}{\cos^2 x+3\cos x2}$
$\displaystyle =\dfrac{\cos x(cos x2)}{(\cos^2 x3\cos x+2)}$
$\displaystyle =\dfrac{\cos x(cos x2)}{(\cos^2 x3\cos x+2)}$
factorize the denominator and change all cosx into secx..

That makes sense now, thank you! :D