buktikanlah identitas trigonometri berikut:
Matematika
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Pertanyaan
buktikanlah identitas trigonometri berikut:
1 Jawaban
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1. Jawaban MuhTaufiqMukhtar
1.
sin x (cot x + tan x)
= sin x ( cosx/sinx + sinx/cosx )
= cos x + (sin²x/cosx)
= cos²x/cosx + sin²x/cosx
= (cos²x + sin²x)/cosx = 1/cos x
b. (1+sinx)/cosx + cosx/(1+sinx)
= (1+2sinx + sin²x +cos²x)/cosx( 1+sinx)
= (2+2sinx)/cosx(1+sinx)
= 2(1+sinx)/cosx(1+sinx)
= 2/cosx
= 2 sec x