Hey, I have a few questions I just can't seem to get down, looking for some help here...
1) sin2x = 2csc2x-tanx
1-cos2x
2) cos(x+y)cos(x-y)=(cosx)^2 +(cosy)^2 -1
3) (cosx)^6 + (sinx)^6 = 1-3(sinx)^2 + 3(sinx)^4
Thanks in advance!
for (3)
$\displaystyle (cosx)^6+(sinx)^6$
$\displaystyle = (cos^{2}x)^3 + (sin^{2}x)^3$
since $\displaystyle (a^3+b^3) = (a+b)(a^2-ab+b^2)$, you can write:
$\displaystyle = (cos^{2}x+sin^{2}x)(cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$
$\displaystyle = 1 (cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$
convert all cosines into sines and your proof will be complete.