急! F4 Basic Trigonometry ex21

1. By the identity (sinx)^2 + (cosx)^2 = 1,
(sinx)^2 = 1 - (13/25)
= 12/25
sinx = (square root 12)/5

tanx= sinx/cosx = (square root 12)/5 * (-5 / square root 13) = - square root (12/13)

2. Divide the whole identity (sinx)^2 + (cosx)^2 = 1 by (sinx)^2,
we get 1 + 1/( (tanx)^2 ) = 1/(sinx)^2
1 + 1/9 = 1/(sinx)^2
sinx = - 3/ square root 10

As tanx = sinx/cosx,
then cosx = sinx/tanx = ( - 3/ square root 10 ) /3 = - 1/ square root 10

3. x= 25degree ,180-25=155degree.

4. (-cosx)(-tanx) / (-sinx)^2 - (cosx)^3 / ( ((sinx)^2) (1/tanx) )
= sinx / (sinx)^2 - (cosx)^3 / ( sinxcosx )
= 1 / sinx - (cosx)^2 / sinx
= (1 - (cosx)^2 ) / sinx
= (sinx)^2 / sinx
=sinx

5. sinx/cosx = 2sinx
sinx=2sinxcosx
0=2sinxcosx-sinx
0=(sinx)(2cosx-1)
sinx=0 or cosx=1/2
x=0,180,360 or x=60, 300
x=0,60,180,300,360