How do you simplify #cot(x+y)+sin(4x+2y)# to trigonometric functions of x and y?

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Answer 1 · 2016-04-12T00:12:31

For this problem, you will make use of the sum and difference identities.

Consider the quotient identity #cottheta = costheta/sintheta#

#(cos(x + y))/(sin(x + y)) + sin(4x + 2y)#

Now, the sum and difference identities:

#sin(A + B) = sinAcosB + cosAsinB#

#cos(A + B) = cosAcosB + sinAsinB#

#(cosxcosy + sinxsiny)/(sinxcosy + cosxsiny) + sin4xcos2y + cos4xsin2y#

Hopefully this helps!