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

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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)   (Show Source): You can put this solution on YOUR website!
Are you sure you didn't mean tan(2x+y)???




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°) =   


 = 

 = 

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

Edwin
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