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Trigonometry> Prove that:- Sin 2 B = Sin 2 A + Sin 2 (A...

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

Abhinav Acharya , 11 Years ago

Grade 11

1 Answers

Sumit Majumdar

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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Last Activity: 11 Years ago

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