Please help! need help with trigonometry and double angle formula

the straight line with equation y=3/4x makes an acute angle theta with the x-axis

the value of tan theta is 3/4

find the value of:
sin 2 theta
cos 2 theta

To simplify the notations, i will write x for theta .

Notice that : 1+(tan x)^2 = [(cos x)^2 + (sin x)^2 ] / (cos x)^2 = 1/(cos x)^2 .

So, (cos x)^2 = 1/(1+(tan x)^2 ) .

So : sin 2x = 2(sin x) *(cos x)

=2 tan x * (cos x)^2 = 2tan x / (1+ (tan x)^2 ) .

Using that tan x=3/4, we obtain :

sin 2x= (3/2) / (1+9/16) = 24/25 .

cos 2x= cos x * cos x -sin x * sin x

= (cos x)^2 -(sin x)^2

= 1/(1+ (tan x)^2 ) - (cos x)^2 * (tan x)^2

= 1/ (1+ (tan x)^2) - (tan x)^2 / (1+ (tan x)^2 )

=[1- (tan x)^2]/ (1+ (tan x)^2 ) .

So cos 2x= (1- 9/16)/ (1+9/16) = 7/25 . :)