Question

sin(a+b)=sinAcosB+cosASinB into sin(a-b)=sinAcosB-cosAsinB​

Answer 1

Answer:

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Step-by-step explanation:

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-cosAsinB

Let sinAcosB=x and cosAsinB=y

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

Substitute x and y

sin(A+B)sin(A-B)

=sin^2Acos^2B-cos^2Asin^2B

=sin^2A(1-sin^2B)-cos^2Asin^2B

=sin^2A-sin^2Asin^2B-cos^2Asin^2B

=sin^2A-(sin^2A+cos^2A)sin2B

=sin^2A-sin^2B

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