Buktikan sin³A+cos³A/1-sinAcosA = sinA+cosA
Matematika
Exeli
Pertanyaan
Buktikan
sin³A+cos³A/1-sinAcosA = sinA+cosA
sin³A+cos³A/1-sinAcosA = sinA+cosA
1 Jawaban
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1. Jawaban DB45
identitas
x³ +y³ = (x+y)(x² - xy + y²)
sin³ A + cos³ A = ( sin A + cos A)(sin² A - sin A cos A + cos² A)
sin³ A +cos³ A = (sin A + cos A)(sin²A+cos² A - sin A cos A)
sin³ A + cos³ A = (sin A + cos A)(1- sin A cos A)
..
(sin³ A + cos³A)/(1 -sin A cos A) =
= (sin A +cos A)(1 -sin A cos A) / (1 - sin A cos A)
= sin A + cos A