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prove cos(45°- A) cos(45°-B) - sin(45°-A)sin(45°-B)=sin(A+B)

prove cos(45°- A) cos(45°-B) - sin(45°-A)sin(45°-B)=sin(A+B)

Grade:12

3 Answers

gokulnath
32 Points
7 years ago
it is equal to cosAcosB-sinAsinB = cos(A+B)
                  hence, = cos(45-A+45-B)
                             = cos(90-(A+B))
                             = sin(A+B)
Khushi kumari
13 Points
3 years ago
Sin(90°-45+A)cos(45°-B) - cos(90°-45+A)Sin(45°-B)
After solving the above equation 
Sin(45°+A-45°+B)
Sin(A+B)
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem.
 
We know, cosXcosY – sinXsinY = cos(X + Y)
Hence,
cos(45° – A) cos(45° – B) – sin(45° – A)sin(45° – B) = cos(45 – A + 45 – B)
                                                                            = cos(90 – (A+B))
                                                                            = sin(A+B)
Hence proved.
 
Thanks and regards,
Kushagra

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