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4sinxsinxsin(x-y)+4sinysinzsin(y-z)+4sinzsinxsin(z-x)=sin(2x-2y)+sin(2y-2z)+sin(2z-2x)

4sinxsinxsin(x-y)+4sinysinzsin(y-z)+4sinzsinxsin(z-x)=sin(2x-2y)+sin(2y-2z)+sin(2z-2x)
 
 

Grade:11

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
LHS
 
4 sinx siny sin(x-y) = 4 sinx siny (sinx cosy - cosx siny)
 
 = 4 sin² x siny cosy - 4 sinx cos x sin²y
 = 2 sin² x sin2y - 2 sin²y sin2x
 
Similarly
When we add all the expressions
 
2 sin²x sin2y - 2 sin²y sin2x + 2 sin²y sin2z - 2 sin²z sin2y + 2 sin²z sin2 x - 2 sin²x sin2z
 
Put sin²x like expressions = 1 - cos²x like
 
You will get the RHS
 
In case of any difficulty please feel free to ask.

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