single trigonometric function: sin(x + y) - sin(y) cos(x) / cox(x) * cos(y)

Question

simplify o a single trigonometric function:
sin(x + y) - sin(y) cos(x) / cox(x) * cos(y)

Answer 1

Hi Billy, to simplify the trig function, we need to know the sum / difference formulas for sin(x + y).

 

Sum sin(x + y):

 

sin(x + y) = sin x * cos y + cos x * sin y

 

Replace in original function:

 

(sin(x + y) - sin y * cos x ) / (cos x * cos y)

 

(sin x * cos y + cos x * sin y - sin y * cos x) / (cos x * cos y)

 

(cos x * sin y) cancels out (- sin y * cos x) in the numerator, leaving:

 

(sin x * cos y) / cos x * cos y)

 

cos y cancels out in the numerator and denominator leaving:

 

sin x / cos x, which is tan x.

 

Results:

 

(sin(x + y) - sin y * cos x ) / (cos x * cos y) = tan x

 

Questions?