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cos(3π/4+x) + sin (3π/4 -x) = 0

= cos(3π/4)cosx + sin(3π/4)sinx + sin(3π/4)cosx - cos(3π/4)sinx
= -1/sqrt2cosx + 1/sqrt2sinx + 1/sqrt2cosx - (-1/sqrt2sinx)
I canceled out -1/sqrt2cosx and 1/sqrt2cosx
Now I have
1/sqrt sinx + 1/sqrt2 sinx

And that doesn't equal 0. So where did I go wrong?

Also cos(x+y)cosy + sin(x+y)siny = cosx
I ended up with
(cosxcosy) + sinxsinycosy + (sinxcosy) + cosxsin^2y

I don't know what to do next.

2 answers

Try your sum and difference identities again. I don't believe you've expanded them correctly.

cos(x + y) = cosx * cosy - sinx * siny
cos(x - y) = cosx * cosy + sinx * siny

sin(x + y) = sinx * cosy + cosx * siny
sin(x - y) = sinx * cosy - cosx * siny
cos(3π/4+x)
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