Question

[tex]{ \rm {Nilai \: dari}}\: \frac{ \tan45 \degree. \cos60 \degree - \: \sin30 \degree. \cos30 \degree}{ \sin60 \degree}[/tex]
[tex] \\ [/tex]
[tex]a). \: \frac{1}{2} \sqrt{3} - \frac{1}{2} [/tex]
ㅤㅤㅤㅤㅤㅤ
[tex]b). \: \frac{1}{2} \sqrt{3} - \frac{1}{3} [/tex]
ㅤㅤㅤㅤㅤㅤ
[tex]c ).\: \frac{1}{3} \sqrt{3} - \frac{1}{2} [/tex]
ㅤㅤㅤㅤㅤㅤ
[tex]d). \: \frac{1}{2} \sqrt{2} - \frac{1}{2} [/tex]
ㅤㅤㅤㅤㅤㅤ
[tex]e). \: \frac{1}{3} \sqrt{2} - \frac{1}{3} [/tex]
[tex] \\ [/tex]
_ _ _ _ _ _ _ _ _ ​

Answer 1

Verified answer

Materi : Trigonometri

Nilai sudut istimewa dalam trigonometri

sin 30° = ½

sin 45° = √2/2

sin 60° = √3/2

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cos 30° = √3/2

cos 45° = √2/2

cos 60° = ½

---

tan x = sin x /cos x

Penyelesaian

( tan 45° . cos 60° - sin 30° . cos 30° )/sin 60°

= ( sin 45/cos 45 . ½ - ½ . √3/2 )/√3/2

= ( 1 . ½ - √3/4 ) × 2/√3

= ( 1 - √3/2 )/√3

= √3( 1 - √3/2 )/(√3)²

= ( √3 - √9/2 )/3

= ⅓√3 - ½

[tex]{ \rm {Nilai \: dari}}\: \frac{ \tan45 \degree. \cos60 \degree - \: \sin30 \degree. \cos30 \degree}{ \sin60 \degree}[/tex]

[tex] \\ [/tex]

[tex]a). \: \frac{1}{2} \sqrt{3} - \frac{1}{2} [/tex]

ㅤㅤㅤㅤㅤㅤ

[tex]b). \: \frac{1}{2} \sqrt{3} - \frac{1}{3} [/tex]

ㅤㅤㅤㅤㅤㅤ

[tex]c ).\: \frac{1}{3} \sqrt{3} - \frac{1}{2} [/tex]

ㅤㅤㅤㅤㅤㅤ

[tex]d). \: \frac{1}{2} \sqrt{2} - \frac{1}{2} [/tex]

ㅤㅤㅤㅤㅤㅤ

[tex]e). \: \frac{1}{3} \sqrt{2} - \frac{1}{3} [/tex]

[tex][/tex]

Maka Jawabannya adalah c. ⅓√3 - ½

Semoga bisa membantu

[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]

Answer 2

trigonometri

sudut istimewa

cos 60°/sin 60° = cotan 60° = 1/3 √3

sin 30° = 1/2

tan 45° = 1

•

[tex] \displaystyle \tt\frac{ \tan45 \degree. \cos60 \degree - \: \sin30 \degree. \cos30 \degree}{ \sin60 \degree} & = \displaystyle \tt 1 \: \times \: cotan \: 60 \degree \: - \: sin \: 30 \degree \\ \\ & = \: \frac{1}{3} \sqrt{3} \: - \: \frac{1}{2} [/tex]