Bentuk berikut yg ekuivalen dg sin x / 1+ cos x + 1+cos x /sin x adlah
Jawab:
Penjelasan dengan langkah-langkah:
trigonometri
__
soal
Penjelasan dengan langkah-langkah:
trigonometri
__
soal
begin{gathered}sf dfrac{sin ~ x}{1 + cos~ x} + dfrac{1+ cos ~ x}{sin ~ x}=sf\\\sf dfrac{sin ~ x(sin ~ x) + (1 +cos~ x)(1 + cos~ x)}{sin ~ x(1 + cos~ x)} sf\\\sf dfrac{sin^2 ~ x + 1 +cos^2~ x+ 2 cos ~ x}{sin ~ x(1 + cos~ x)} sf\\\sf dfrac{(sin^2 ~ x +cos^2~ x)+1 + 2 cos ~ x}{sin ~ x(1 + cos~ x)} sf\\\sf dfrac{1+1 + 2 cos ~ x}{sin ~ x(1 + cos~ x)} sf\\\sf dfrac{2 + 2 cos ~ x}{sin ~ x(1 + cos~ x)} sf\\end{gathered}
1+cos x
sin x
+
sin x
1+cos x
=
sin x(1+cos x)
sin x(sin x)+(1+cos x)(1+cos x)
sin x(1+cos x)
sin
2
x+1+cos
2
x+2cos x
sin x(1+cos x)
(sin
2
x+cos
2
x)+1+2cos x
sin x(1+cos x)
1+1+2cos x
sin x(1+cos x)
2+2cos x
begin{gathered}sf dfrac{2 (1 + cos ~ x)}{sin ~ x(1 + cos~ x)} sf\\\sf dfrac{2}{sin~ x} = 2(dfrac{1}{sin~ x})= 2~cosec ~ xend{gathered}
sin x(1+cos x)
2(1+cos x)
sin x
2
=2(
sin x
1
)=2 cosec x