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Prove that:- Sin 2 B = Sin 2 A + Sin 2 (A-B) – 2SinAcosBsin(A-B)

Prove that:-
Sin2B = Sin2A + Sin2(A-B) – 2SinAcosBsin(A-B)

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
8 years ago
Dear student,
We have:
\left (sin\left ( A \right )cos\left ( B \right )-sin\left ( A-B \right ) \right )^{2}=sin^{2}\left ( A \right )cos^{2}\left ( B \right )+sin^{2}\left ( A-B \right )-2sin\left ( A-B \right )sin\left ( A \right )cos\left ( B \right )=sin^{2}\left ( A \right )\left ( 1-sin^{2}\left ( B \right ) \right )+sin^{2}\left ( A-B \right )-2sin\left ( A-B \right )sin\left ( A \right )cos\left ( B \right )Hence the result.
Thanks & Regards
Sumit Majumdar,
askIITians Faculty
Ph.D,IIT Delhi

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