SOLUTION: Show that sin²x + sin²y + 2sinxsinycos(x+y) = sin²(x+y)

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Question 1139613: Show that sin²x + sin²y + 2sinxsinycos(x+y) = sin²(x+y)
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Let this be any triangle:



By the law of cosines:

(1)     

By the law of sines:

        

Let those equal to k

        

Then we have 

         

Substitute in (1)

        

        

        

Divide through by k2:

        

Since x + y + z = 180°, z = 180°-x-y = 180°-(x+y)

Use the identities , and :

          

        

        

Edwin

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Above is your solved problem!

Edwin


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