Given that tan x = 5/12
To find cos(180-x)
we know that cos(180-x) = -cos x
The fundamental formula in trigonometry says that:
sin2 x+cos2 x=1
If we divide the above formula with cos2 x
(sin2 x)/(cos2 x) + 1= 1/(cos2x)
But we know the fact that the tangent function is the ratio between sin x/cos x, so (sin2 x)/(cos2 x) = tan2 x
tan2 x + 1 = 1/(cos2 x)
(cos2 x)(tan2 x + 1) = 1
cos2 x = 1/(tan2 x + 1)
cos x = [1/(tan2 x + 1)]1/2
cos x = {[1/[(5/12)2 + 1])}1/2
cos x = {[1/[(25/144) + 1])}1/2
cos x = [1/(169/144)]1/2
cos x = (144/169)1/2
cos x = 12/13
Hence, cos(180-x) = -cos x = -12/13
