prove that : sin^2 (A+B) - sin^2(A-B) = sin2A . sin2B

Asked by medha painuly | 27th May, 2014, 05:13: PM

Expert Answer:

W e space n e e d space t o space p r o v e space t h a t space sin squared open parentheses A plus B close parentheses minus sin squared open parentheses A minus B close parentheses equals sin 2 A cross times sin 2 B L e t space u s space c o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space a b o v e space e q u a t i o n. T h u s comma space sin squared open parentheses A plus B close parentheses minus sin squared open parentheses A minus B close parentheses equals open square brackets sin A cos B plus cos A sin B close square brackets squared minus open square brackets sin A cos B minus cos A sin B close square brackets squared equals open square brackets sin squared A cos squared B plus cos squared A sin squared B plus 2 sin A cos B cos A sin B close square brackets space space space space space space minus open square brackets sin squared A cos squared B plus cos squared A sin squared B minus 2 sin A cos B cos A sin B close square brackets equals sin squared A cos squared B plus cos squared A sin squared B plus 2 sin A cos B cos A sin B minus sin squared A cos squared B minus cos squared A sin squared B plus 2 sin A cos B cos A sin B equals 4 sin A cos B cos A sin B equals 2 sin A cos A cross times 2 sin B cos b equals sin 2 A cross times sin 2 B equals R. H. S. H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 28th May, 2014, 09:10: AM