Buktikan identitas dari persamaan berikut 1. Tan2 α / 1+sec α = sec α -1 2. ( sin α - cos α)2 = 2 - ( sin α + cos α)2
Matematika
rizzky28
Pertanyaan
Buktikan identitas dari persamaan berikut
1. Tan2 α / 1+sec α = sec α -1
2. ( sin α - cos α)2 = 2 - ( sin α + cos α)2
1. Tan2 α / 1+sec α = sec α -1
2. ( sin α - cos α)2 = 2 - ( sin α + cos α)2
1 Jawaban
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1. Jawaban Robinn
1.
tan²x / 1+secx = secx - 1
(sec²x - 1) / (1 + secx) = secx - 1
(secx-1)(secx+1) / (1 + secx) = secx - 1
secx - 1 = secx - 1
2.
(sinx - cosx)² = 2 - ( sinx + cosx )²
sin²x - 2sinxcosx + cos²x =2 - (sinx+cosx)²
1 - 2sinxcosx = 2 - (sin²x + 2sinxcosx + cos²x)
1 - 2sinxcosx = 2 - (1 + 2sinxcosx)
1 - 2sinxcosx = 2 - 1 - 2sinxcosx
1 - 2sinxcosx = 1 - 2sinxcosx