We have: #tan(x + 45^(circ))#
If you are trying to expand this expression, you can use the angle sum identity for #tan(x)#; #tan(x + y) = frac(tan(x) + tan(y))(1 - tan(x) tan(y))#:
#Rightarrow tan(x + 45^(circ)) = frac(tan(x) + tan(45^(circ)))(1 - tan(x) tan(45^(circ)))#
Let's apply the common trigonometric ratio #tan(45^(circ)) = 1#:
#Rightarrow tan(x + 45^(circ)) = frac(tan(x) + 1)(1 - tan(x) cdot 1)#
#Rightarrow tan(x + 45^(circ)) = frac(tan(x) + 1)(1 - tan(x))#
#Rightarrow tan(x + 45^(circ)) = frac(tan(x) + 1)(- (tan(x) - 1))#
#therefore tan(x + 45^(circ)) = - frac(tan(x) + 1)(tan(x) - 1)#
