Question

sin(A+B)sin(A-B)=sin^2A-sin^2B

Answer 1

i hope this will help you

Answer 2

Hello users....

We have to prove that
Sin(A+B)sin(A-B)=sin²A-sin²B

Solution:-
Formula used
a²-b²= (a+b)(a-b)
And
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
= RHS

⭐⭐ Hope it helps ⭐⭐