buktikan bahwa sin (A+B) sin (A-B) = sin^2 A- sin^2 B
Matematika
Jhendyra
Pertanyaan
buktikan bahwa sin (A+B) sin (A-B) = sin^2 A- sin^2 B
1 Jawaban
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1. Jawaban brillianalifia
sin (a+b) sin (a-b)
=(sin a cos b + cos a sin b)(sin a cos b - cos a sin b)
=sin^2 a cos^b - sin a cos b cos a sin b + sin a cos b cos a sin b - cos^2 a sin^2 b
=sin^2 a cos^b - cos^2 a sin^2 b
=sin^2 a (1-sin^2 b) - (1-sin^2 a) sin^2 b
=sin^2 a - sin^2 a sin^2b - sin^2 b + sin^2a sin^2b
=sin^2 a - sin^2 b
TERBUKTI