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put this solution on YOUR website! .
Prove that
sin (x+1)A .sin (x+2)A +cos(x+1)A .cos (x+2)A=cosA
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There is a trigonometric identity
sin(x)*sin(y) + cos(x)*cos(y) = cos(x-y),
valid for all angles x and y.
Are you familiar with it?
If not, you can read the lesson Addition and subtraction formulas in this site.
Simply apply this formula. You will get
sin((x+1)A).sin((x+2)A) +cos((x+1)A).cos((x+2)A) = cos( (x+1)A - (x+2)A ) = cos(-A) = cos(A).
That's all.
