SOLUTION: If x+y is less than 90 degree and sin(2x-20degree)= cos(y-10 degree) then find tan(x+y)

Algebra ->  Trigonometry-basics -> SOLUTION: If x+y is less than 90 degree and sin(2x-20degree)= cos(y-10 degree) then find tan(x+y)      Log On


   

Question 1015107: If x+y is less than 90 degree and sin(2x-20degree)= cos(y-10 degree) then find tan(x+y)
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure you didn't mean tan(2x+y)???


y+=+2+%28%22180%B0%22n-x%2B%2260%B0%22%29

Use the identity:

If sin(A) = cos(B), then A = 90°-B+360°n

sin(2x-20°)= cos(y-10°)

2x-20°= 90°-(y-10°)+360°n

2x-20°= 90°+y+10°+360°n

2x-20°= 100°+y+360°n

2x = 120°+y+360°n

2x-120°-360°n = y

x+y = x+(2x-120°-360°n)

x+y = 3x-120°-360°n 

tan(x+y) = tan(3x-120°-360°n)

tan(x+y) = tan(3x-120°) = %28+tan%283x%29-tan%28%22120%B0%22%29+%29%2F%28+1%2Btan%283x%29tan%28%22120%B0%22%29+%29  


 = %28+tan%283x%29-%28-sqrt%283%29%29+%29%2F%28+1%2Btan%283x%29%28-sqrt%283%29%29+%29

 = %28+tan%283x%29%2Bsqrt%283%29+%29%2F%28+1-tan%283x%29%28sqrt%283%29%29+%29

tan(2x+y) works out much nicer.

Edwin