Asked by justme
pls. help:
prove the identity
sin2x+sin2y=2sin(x+y)cos(x-y)
prove the identity
sin2x+sin2y=2sin(x+y)cos(x-y)
Answers
Answered by
Reiny
LS = 2sinxcosx + 2 sinycosy
= 2[sinxcosx + sinycosy}
RS = 2[sinxcosy + cosxsiny][cosxcosy + sinxsiny]
= 2[ sinxcosxcos^2 y + sin^2 xcosysiny + cos^2 xsinycosy + sinxcosxsin^2 y]
= 2[sinxcosx(cos^2y + sin^2y) + cosysiny(sin^2x + cos^2x) ]
= 2[ sinxcosx + sinycosy]
= LS
please check my typing
= 2[sinxcosx + sinycosy}
RS = 2[sinxcosy + cosxsiny][cosxcosy + sinxsiny]
= 2[ sinxcosxcos^2 y + sin^2 xcosysiny + cos^2 xsinycosy + sinxcosxsin^2 y]
= 2[sinxcosx(cos^2y + sin^2y) + cosysiny(sin^2x + cos^2x) ]
= 2[ sinxcosx + sinycosy]
= LS
please check my typing
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