SOLUTION: Prove that sin (x+1)A .sin (x+2)A +cos(x+1)A .cos (x+2)A=cosA

Question 1062381: Prove that
sin (x+1)A .sin (x+2)A +cos(x+1)A .cos (x+2)A=cosA
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
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Prove that
sin (x+1)A .sin (x+2)A +cos(x+1)A .cos (x+2)A=cosA
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

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