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Is Sin(A+B).Sin(A-B) = Sin^2A - Sin^2B = Cos^2B - Cos^2A If yes, how??

Is Sin(A+B).Sin(A-B) = Sin^2A - Sin^2B
                                     = Cos^2B - Cos^2A
If yes, how?? 

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
Sin(a+b) = sin acos b + cos a sin b 
And 
Sin(a-b) = sin acos b - cos a sinb 
And 
Sin²x+cos²x = 1
Now ,
Taking LHS 
Sin(A+B)sin(A-B) 
= ( sin Acos B + cos A sin B) (sin Acos B - cos A sin B)
= (Sin²Acos²B) - (sin²Bcos²A)
= Sin²A(1-Sin²B ) - Sin²Bcos²A
= Sin²A - sin²Asin²B -sin²Bcos²A
= Sin²A - sin²B (sin²A + cos² A)
= Sin²A - sin²B
 

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