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

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.