You should know the following trigonometric identities.

(A)$\displaystyle sin(-x)=-sinx$

(B)$\displaystyle cos(-x)=cosx$

(C)$\displaystyle cos(x+y)=cosxcosy-sinxsin y$

(D)$\displaystyle sin(x+y)=sinxcosy+cosxsin y$

Use theseto derive the followingimportantidentities, which you should also know.

(a)$\displaystyle sin^2x+cos^2x=1$ (use C and $\displaystyle cos0=1$

(b)$\displaystyle sin2x=2sinxcosx$

(c)$\displaystyle cos2x=cos^2x-sin^2x$

(d)$\displaystyle cos2x=2cos^2x-1$

(e)$\displaystyle cos2x=1-2sin^2x$

(f)$\displaystyle |cos\frac{x}{2}|=\sqrt{\frac{1+cosx}{2}}$

(g)$\displaystyle |sin\frac{x}{2}|=\sqrt{\frac{1-cosx}{2}}$

If anybody can finish these would be a tremendous help to me

took me over 30min just to write this in latex form... sigh...

i really hope someone will reply on how to do these with 1 or 2 as a example so i can do the rest

Thanks in advance