1) Solve
(sinx)/(cot^2x) - (sinx)/(cos^2x)
2) Prove
tan^2x - sin^2x = tan^2x*sin^2x
3) Prove
sin(x - π/2) = -cosx
Thanks for any help!
#1 can only be simplified ... it's not an equation.
$\displaystyle \sin{x}\left(\frac{1}{\cot^2{x}} - \frac{1}{\cos^2{x}}\right)$
$\displaystyle \sin{x}(\tan^2{x} - \sec^2{x})$
$\displaystyle \sin{x}[\tan^2{x} - (1 + \tan^2{x})] = -\sin{x}$
#2 change the right side to $\displaystyle \tan^2{x}(1 - \cos^2{x})$ ... work from there to get the left side.
#3 use the difference identity for sine on the left side ...
$\displaystyle \sin(a - b) = \sin(a)\cos(b) - \cos(a)\sin(b)
$