Find the exact values of sin ( 2 x ) , cos ( 2 x ) and tan ( 2 x ) without solving for x . If tan x = 6 , and x is in quadrant 1 .

Answer 1

Draw a right triangle with acute angle x. let 6 be the length of the side opposite x and let 1 be the length ofthe side adjacent to x. By the Pythagorean Theorem, the hypotenuse has length √37.

Then, sinx = 6/√37 and cosx = 1/√37.

sin(2x) = 2sinxcosx = 2(6/√37)(1/√37) = 12/37

cos(2x) = cos²x - sin²x = 1/37 - 36/37 = -35/37

tan(2x) = sin(2x) / cos(2x) = -12/35

Answer 2

tan(2x)=sin(2x)/cos(2x)

sin=tan*cos

cos=sin/tan

Without using the angle(β); this is the best I can do.