prove .. sin (x+y) cos (x-y) = sinx/Secx + cosx/cscx

Question

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Answer 1

Looking at the right side we see that sin(x)/sec(x) + cos(y)/csc(y) = sin(x)cos(x) + cos(y)sin(y) since sec(x)=1/sin(x) and csc(y)=1/cos(y).

 

Working with the left side you first need to replace the sin(x+y) with sin(c)cos(y) + cos(x)sin(y) and cos(x-y) with cos(x)cos(y) + sin(x)sin(y).

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Now do the multiplication and factor in terms of cos²+sin² which equals 1 and you will have the right side.

 

If you have to prove that the left side evolves into the right side just follow the logic of the left side.