Penjelasan dengan langkah-langkah:
1. (sin 60° - sin 30°)/(cos 60° - cos 30°)
= (√3/2 - 1/2)/(1/2 - √3/2)
= ((√3 - 1)/2)/((1 - √3)/2)
= (√3 - 1)/(1 - √3) → rasionalkan
= (√3 - 1)/(1 - √3) . (1 + √3)/(1 + √3)
= (√3 - 1)(1 + √3)/(1 - √3)(1 + √3)
= (√3 + 3 - 1 - √3)/(1 - 3)
= 2/(-2)
= -1
2. (sin 60° - tan 30°)/(cotan 60° + cos 30°)
= (√3/2 - √3/3)/(√3/3 + √3/2)
= ((√3 . 3 - 2 . √3)/6)/((√3 . 2 + 3 . √3)/6)
= ((3√3 - 2√3)/6)/((2√3 + 3√3/6)
= (√3/6)/(5√3/6)
= √3/5√3
= 1/5
4.
sin 60° = cos 30° = √3/2
sin 30° = cos 60° = 1/2
maka
[tex] \frac{ \frac{ \sqrt{3} }{2} - \frac{1}{2} }{ \frac{1}{2} - \frac{ \sqrt{3} }{2} } = \frac{ \frac{ \sqrt{3} - 1 }{2} }{ \frac{1 - \sqrt{3} }{2} } = - 1[/tex]
5.
sin 60° = cos 30°= √3/2
Tan 30° = cot 60° = √3/3
[tex] \frac{ \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{3} }{ \frac{ \sqrt{3} }{3} + \frac{ \sqrt{ 3} }{2} } = \frac{ 1 }{5} [/tex]
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Verified answer
Penjelasan dengan langkah-langkah:
1. (sin 60° - sin 30°)/(cos 60° - cos 30°)
= (√3/2 - 1/2)/(1/2 - √3/2)
= ((√3 - 1)/2)/((1 - √3)/2)
= (√3 - 1)/(1 - √3) → rasionalkan
= (√3 - 1)/(1 - √3) . (1 + √3)/(1 + √3)
= (√3 - 1)(1 + √3)/(1 - √3)(1 + √3)
= (√3 + 3 - 1 - √3)/(1 - 3)
= 2/(-2)
= -1
2. (sin 60° - tan 30°)/(cotan 60° + cos 30°)
= (√3/2 - √3/3)/(√3/3 + √3/2)
= ((√3 . 3 - 2 . √3)/6)/((√3 . 2 + 3 . √3)/6)
= ((3√3 - 2√3)/6)/((2√3 + 3√3/6)
= (√3/6)/(5√3/6)
= √3/5√3
= 1/5
Penjelasan dengan langkah-langkah:
4.
sin 60° = cos 30° = √3/2
sin 30° = cos 60° = 1/2
maka
[tex] \frac{ \frac{ \sqrt{3} }{2} - \frac{1}{2} }{ \frac{1}{2} - \frac{ \sqrt{3} }{2} } = \frac{ \frac{ \sqrt{3} - 1 }{2} }{ \frac{1 - \sqrt{3} }{2} } = - 1[/tex]
5.
sin 60° = cos 30°= √3/2
Tan 30° = cot 60° = √3/3
maka
[tex] \frac{ \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{3} }{ \frac{ \sqrt{3} }{3} + \frac{ \sqrt{ 3} }{2} } = \frac{ 1 }{5} [/tex]