SOLUTION: verify the trigonometric identity: (sinx-siny/cosx+cosy)+(cosx-cosy/sinx+siny)=0

Question 204702: verify the trigonometric identity:
(sinx-siny/cosx+cosy)+(cosx-cosy/sinx+siny)=0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
verify the trigonometric identity:
(sinx-siny/cosx+cosy)+(cosx-cosy/sinx+siny)=0
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Multiply thru by (cosx+cosy)(sinx+siny) to get:
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(sinx-siny)(sinx+siny) + (cosx-cosy)(cosx+cosy) = 0
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Multiply to get:
(sin^2x-sin^2y) + (cos^2x-cos^2y) = 0
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Substitute 1-sin^2 for each sin^2 to get:
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sin^2x-sin^2y + 1-sin^2x -(1 - sin^2y) = 0
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Notice that the left side is zero.
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Cheers,
Stan H.
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