Find sin2x ,cos2x , and tan2x if cosx=1/sqrt5 and x terminates in quadrant 1.

Answer 1

Hi,

cosx=1/sqrt5 = 1/ √5

First you need to find sinx and also you know all sin,cos,tan,and cot at first quadrant are positive

sin^2x + cos^2x = 1 ====> sin^2x = 1 - ( 1/√5 )^2 = 1 - 1/5 = 4/5 ====> sinx = 2/√5

Tanx = sinx / cos x = (2/√5) / (1/√5)= 2

sin 2x = 2 sinx *cosx = 2 (2/√5 ) ( 1/√5) = 4/5

cos 2x = cos^2 x - sin^2 x = 1/5 - 4/5 = -3/5

tan2x = sin2x / cos2x = (4/5 ) / (-3/5) = -4/3 or you can use this formula:

tan 2x = ( 2tanx ) / ( 1- tan^2 x) that by replacing tanx = 2 you have the same answer.

I hope it is useful,

Minoo