1.

Given that y=2$\displaystyle sin^3$ x - 3 sin x, find an expression for $\displaystyle \frac{dy}{dx}$ in terms of cos x and then find $\displaystyle \frac{d^2y}{dx^2}$.

2.

The diagram shows an isosceles triangle ABC inscribed in a circle of radius r cm and centre at

*O*. Given that $\displaystyle \angle {BAO}$=$\displaystyle \theta$ radian and $\displaystyle \angle$ ADC = $\displaystyle \frac{\pi}{2}$ radians,

**show** that area , S $\displaystyle cm^2$, of triangle ABC is given by S = $\displaystyle r^2$ sin 2$\displaystyle \theta$(1+ cos 2$\displaystyle \theta$).

for the first question, what i tried to do:

$\displaystyle \frac{dy}{dx}$

= 6($\displaystyle sin^2$ x)($\displaystyle cos^2$ x) - 3 cos x

=3 cos x [ 2 $\displaystyle sin^2$ x cos x -1]

then.....how do i continue to simplify it?the answer is 3 cos x(1- 2 $\displaystyle cos^2$ x)......

for question 2 ....

AB= $\displaystyle \frac{2r}{cos \theta}$ S

= ($\displaystyle \frac{1}{2}$)($\displaystyle \frac{2r}{cos \theta}$)($\displaystyle \frac{2r}{cos \theta}$)sin 2$\displaystyle \theta$

=($\displaystyle \frac{2r^2}{cos^2 \theta}$) sin 2$\displaystyle \theta$

and......then....how do i simplify it to $\displaystyle r^2$sin 2$\displaystyle \theta$(1+ cos 2$\displaystyle \theta$)....??? is my working correct in first place???
any help is much appreciated. thanks in advance.