Is Sin(A+B).Sin(A-B) = Sin^2A - Sin^2B = Cos^2B -

Question

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

Arun · Accepted Answer

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

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