Prove that sin(a+b)sin(a-b)=sin^2a-sin^2b

1.	Prove that sin(a+b)sin(a-b)=sin^2a-sin^2b
Answer» <html><body><p>-<a href="https://interviewquestions.tuteehub.com/tag/step-25533" style="font-weight:bold;" target="_blank" title="Click to know more about STEP">STEP</a> explanation:sin(A + <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>)sin(A − B) = sin² A – sin² B -LHS= sin(A + B)sin(A - B)Recall: sin(a - b) = sin a <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> ß- cos a sin And sin(a + 3) = sin a cos 3 + cos a sin 3(sin A cos B+ cos A sin B)<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> (sin A cos B - cos A sin B) = sin² A cos² B - cos² A sin² BRecall: sin² a + cos² a = <a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a> From above, we can then assume correctly that:sin² a = 1 cos² a AND -- cos² a = 1 - sin² a= sin² A (1 - sin² B) – sin² B(1 – sin² A)sin² A - sin² A sin² B – sin² B + sin² A sin² B= sin² A - sin² B= RHS</p></body></html>

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