50 poin + 25 poin Identitas Trigonometri Buktikan : ◆> sinθ / 1+cos θ + 1+cos θ / sin θ = 2/sin θ ◆> csc (180°+A) . csc (180°-A) - tan (90° + A) .cot(180° + A )

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Misal :
a = sin x
b = 1 + cos x

a/b + b/a
= (a² + b²)/(ab)
= (sin² x + 1 + cos² x + 2 cos x) / sin x (1 + cos x)
= 2(1 + cos x) / sin x (1 + cos x)
= 2/sin x
TerBukTi

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csc (180° + A) . csc (180° - A) - tan (90° + A) . cot (180° + A)
= -csc A . csc A - (-cot A) . tan A
= -csc² A + 1
= 1 - csc² A
= (sin² A - 1)/sin² A
= -cos² A /sin² A
= -cot A