Another Trig question

cosx=sin(90-x) (identity)

so,

cos(x+60)=sin(90-x-60)

giving,

sin(90-x-60)=sin(45+x)

therefore,

30-x=45+x
-15=2x
x=-7.5 deg.

when I substitute x=-7.5 into the equation I get
cos(-7.5+60)=sin(45--7.5)
cos(52.5)=sin(52.5)
-0.616052331=0.787705227

Just in case one question wasnt enough heres another one!

Cos(x+60) = Sin (45-x)
cosxcos60-sinxsin60 =sin45cosx-cos45sinx
.5cosx-(root3/2) =(1/root 2)-.5cosx
(-root3/2 +1/root2)sinx =(1/root2-.5)cosx
sinx/cosx
tanx = (-root3/2+1/root2) / (1/root2-.5)

Then solve as normal.

Does my method look vaguely right to anyone. Thanks in advance

I get tan x=-1.29

u may have rounded a little as i got -1.30 using the accurate values

Cos(x+60) = Sin (45-x)

CosxCos60 - SinxSin60 = sin45cosx - coz45sinx
1/2cosx - sqrt3/2sinx = 1/sqrt2cosx - 1/sqrt2sinx
cosx (1/2-1/sqrt2) = sinx (sqrt3/2 - 1/sqrt2)
tanx = (sqrt3/2 - 1/sqrt2)/(1/2-1/sqrt2)

tan x =0.158918622/-0.207106781
tan x= -0.767326....

x = -37.5degrees (1dp) And other values depending on the range