If tanx = 4/3 what is cos (2x)?

Question

Also please add the formulas you can use to find cos(2x)

Answer 1

If you dig the trigonometric formulas, you will find this identity:

 

tan² x =(1 - cos 2x)/(1 +cos 2x).

 

The rest is simple algebra, solving equation using equivalent transformations:

(4/3)² = (1 - cos 2x)/(1 +cos 2x),

(16/9)(1 + cos 2x) = 1 - cos 2x,

16/9 +16/9•cos 2x = 1 - cos 2x,

16/9 - 1 = cos 2x(-1 - 16/9),

7/9 = cos 2x (- 25/9),

cos 2x = -(7/9)/(25/9),

cos 2x = -7/25.

Answer 2

If tan x = 4/3, then cos x = 3/5 and sin x = 4/5. (Draw a right triangle and label the part t see why.)

 

cos 2x = cos²x - sin²x => cos 2x = -7/25.

 

You can, of course, simply look up arctan (4/3), double it and then  look up the cos of that angle.