Hey guys I need some help with these two different equations. It is to simplify the expressions:
Equation 1:
9sinx/cos^2x * cosxsinx-3cosx/sin^2x-9
and the second equation is:
sin^4xcosx/cos^4xsinx
Thanks in advance!!
Hello, DjNito!
These require basic Algebra (factoring and reducing).
Exactly where is your difficulty?
These are not equations . . . they are expressions.
Be precise.
$\displaystyle \frac{9\sin x}{\cos^2\!x}\cdot \frac{\cos x\sin x - 3\cos x}{\sin^2\!x - 9} $
Factor: .$\displaystyle \frac{9\sin x}{\cos^2\!x}\cdot \frac{\cos x(\sin x - 3)}{(\sin x - 3)(\sin x + 3)}$
Reduce: .$\displaystyle \frac{9\sin x}{\cos x(\sin x + 3)}$
$\displaystyle \frac{\sin^4\!x\cos x}{\cos^4\!x\sin x}$
Reduce: .$\displaystyle \frac{\sin^4x\cos x}{\sin x\cos^4\!x} \;=\;\frac{\sin^3\!x}{\cos^3\!x}$
Simplify: .$\displaystyle \left(\frac{\sin x}{\cos x}\right)^3 \;=\;\tan^3\!x$