Question

prove that cos(a+b)cos(a-b)=cos²a-sin²b=cos²b-sin²a​

Answer 1

Solution:-

Taking L.H.S,

cos(A+B)cos(A-B)

=(cosA cosB+sinA+sinB).(cosA cosB-sinA sinB)

=cos²A cos²B - sin²A sin²B

=cos²A (1-sin² B)-(1-cos²A) sin²B

=cos²A-cos²A sin²B-sin²B+cos²A sin²B

=cos²A- sin²B

=(1-sin²A)-(1-cos²B)

=1-sin²A-1+cos²B

=cos²B- sin²A [Proved]

Some formulas:-

•sin(A+B)=sinA cosB + cosA sinB

•sin(A-B)=sinA cosB - cosA sinB

•cos(A+B)= cosA cosB - sinA sinB

•cos(A-B)= cosA cosB + sinA sinB

Hope it will help you.