Question 422417
Given that sinx(cosy + 2siny) - cosx(2cosy-siny) = 0, find the value of tan(x+y)

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        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</pre>