Given that sinx(cosy + 2siny) - cosx(2cosy-siny) = 0, find the value of tan(x+y)
sinx(cosy + 2siny) - cosx(2cosy - sin y) = 0
Remove the parentheses:
sinx*cosy + 2sinx*siny - 2cosx*cosy + cosx*siny = 0
Rearrange the terms:
sinx*cosy + cosx*siny - 2cosx*cosy + 2sinx*siny = 0
Factor -2 out of the 3rd and 4th terms:
sinx*cosy + cosx*siny - 2(cosx*cosy - sinx*siny) = 0
Use the identity sin(A + B)=sinA*cosB + cosA*sinB to rewrite the
first two terms:
sin(x + y) - 2(cosx*cosy - sinx*siny) = 0
Use the identity cos(A + B)=cosA*cosB - sinA*sinB to rewrite the
two terms inside the parenthese:
sin(x + y) - 2*cos(x + y) = 0
Divide through by cos(x + y)
sin(x + y) 2*cos(x + y) 0
覧覧覧覧覧 - 覧覧覧覧覧覧 = 覧覧覧覧覧
cos(x + y) cos(x + y) cos(x + y)
sin(A)
Use the identity 覧覧覧 = tan(A)
cos(A)
to rewrite the first term, and simplify the other terms:
tan(x + y) - 2 = 0
tan(x + y) = 2
Edwin