Question #2fb5f
1 Answer
Apply the Sum and Difference Formulas for Sine and Cosine functions:
#sin(x+y) = sin(x)cos(y)+cos(x)sin(y)#
#sin(x-y) = sin(x)cos(y)-cos(x)sin(y)#
#cos(x+y) =cos(x)cos(y) -sin(x)sin(y)#
#cos(x-y) =cos(x)cos(y) +sin(x)sin(y)#
We'll attempt to evaluate the numerator and denominator separately to avoid excessively large expressions:
Numerator:
#=color(red)(sin(x)cos(y)+cos(x)sin(y))+color(blue)(sin(x)cos(y)-cos(x)sin(y))#
#= 2sin(x)cos(y)#
Denominator:
#=color(red)(cos(x)cos(y) -sin(x)sin(y)) +color(blue)(cos(x)cos(y) +sin(x)sin(y))#
#=2cos(x)cos(y)#
Left-side of Equation
# (cancel(2)sin(x)cancel(cos(y)))/(cancel(2)cos(x)cancel(cos(y)))#
#=tan(x)#
