# 2 cos(x+45)=1The question asks to solve trigonometric identities. Give answers to the nearest tenth when necessary.

giorgiana1976 | Student

2 cos(x+45)=1

cos(x+45)=1/2

There are 2 ways of solving from here:

1) either you choose to express (x+45) by it's inverse function, arccos (1/2),

(x+45) = +/- arccos (1/2) + 2k*pi

(x+45) = +/-(pi/3) + 2k*pi, where 45=pi/4

x+pi/4 = -(pi/3) + 2k*pi

x = -(pi/4)-(pi/3) + 2k*pi

x = -7pi/12 + 2k*pi

-7pi/12 = pi/12 + pi/2 = 180/12 + 180/2=15+90=105

or,

x = -(pi/4)+(pi/3) + 2k*pi

x=-pi/12 + 2k*pi

-pi/12=2pi-pi/12=360-15=245 degrees

2) or you could express cos(x+45), through it's formula:

cos(x+45) = cos x cos 45 - sin x sin 45

cos(x+45) = [(sqrt 2)/2](cos x - sin x)

[(sqrt 2)/2](cos x - sin x) = 1/2

cos x - sin x = sqrt 2 / 2, which is a linear equation and it could be by applying the helping angle method.

neela | Student

2cos(x+45) = 1 . Or

cos(x+45) = 1/2 = cos 60. Or cos (-60). Or

x+45 = 60. Or x = 60-45 = 15 degree. Or

x+45 = -60. Or x = -60-45 = -105 degree.