Question

Tan (x+45°)= cosx + sinx/ cosx-sinx

Answer 1

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tan (A+B) = (tan A + tan B) / ( 1 - tan A . tan B)
tan 45 = 1

tan(x+45) = (tan x + tan 45) / 1 - (tan x . tan45)
tan(x+45) = (tan x + 1)/ (1 - tanx) = (tan x + 1)/ -(tan x + 1) = - 1

tan (x+45) = (cos x + sin x)/ (cos x - sin x)
-1 = (cos x + sin x) / (cos x - sin x)
cos x + sin x = -(cos x - sin x)
cos x + sin x = - cos x + sin x
2 cos x = 0
cos x = 0
x = 90°, 180°