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Bentuk cos 7 5 ∘ cosec 7 5 ∘ sin 1 5 ∘ sec 1 5 ∘ setara dengan ...

Bentuk $\frac{sin 1 5 ^{\circ} sec 1 5 ^{\circ}}{cos 7 5 ^{\circ} cosec 7 5 ^{\circ}}$ setara dengan ...

$\frac{sec 7 5 ^{\circ}}{cosec 7 5 ^{\circ}}$
$\frac{sec 1 5 ^{\circ}}{cosec 1 5 ^{\circ}}$
$\frac{sin 1 5 ^{\circ}}{cosec 7 5 ^{\circ}}$
$0$
$1$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali identitas trigonometri: sec θ cosec θ = = c o s θ 1 s i n θ 1 dan ingat kembali pada kuadran I berlaku: sin ( 90 − α ) cos ( 90 − α ) = = cos α sin α sehingga c o s 7 5 ∘ cosec 7 5 ∘ s i n 1 5 ∘ s e c 1 5 ∘ = = = = = = = c o s 7 5 ∘ ⋅ sin 7 5 ∘ 1 s i n 1 5 ∘ ⋅ cos 1 5 ∘ 1 sin 7 5 ∘ cos 7 5 ∘ cos 1 5 ∘ sin 1 5 ∘ c o s 1 5 ∘ s i n 1 5 ∘ × c o s 7 5 ∘ s i n 7 5 ∘ c o s 1 5 ∘ c o s 7 5 ∘ s i n 1 5 ∘ s i n 7 5 ∘ c o s 1 5 ∘ c o s 7 5 ∘ s i n ( 9 0 ∘ − 7 5 ∘ ) s i n ( 9 0 ∘ − 1 5 ∘ ) c o s 1 5 ∘ c o s 7 5 ∘ c o s 7 5 ∘ c o s 1 5 ∘ 1 Oleh karena itu, jawaban yang benar adalah E.

Ingat kembali identitas trigonometri:

$sec θ cosec θ = = \frac{1}{c o s θ} \frac{1}{s i n θ}$

dan ingat kembali pada kuadran I berlaku:

$sin (90 - α) cos (90 - α) = = cos α sin α$

sehingga

$\frac{s i n 1 5 ^{\circ} s e c 1 5 ^{\circ}}{c o s 7 5 ^{\circ} cosec 7 5 ^{\circ}} = = = = = = = \frac{s i n 1 5 ^{\circ} \cdot \frac{1}{cos 1 5 ^{\circ}}}{c o s 7 5 ^{\circ} \cdot \frac{1}{sin 7 5 ^{\circ}}} \frac{\frac{sin 1 5 ^{\circ}}{cos 1 5 ^{\circ}}}{\frac{cos 7 5 ^{\circ}}{sin 7 5 ^{\circ}}} \frac{s i n 1 5 ^{\circ}}{c o s 1 5 ^{\circ}} \times \frac{s i n 7 5 ^{\circ}}{c o s 7 5 ^{\circ}} \frac{s i n 1 5 ^{\circ} s i n 7 5 ^{\circ}}{c o s 1 5 ^{\circ} c o s 7 5 ^{\circ}} \frac{s i n ( 9 0 ^{\circ} - 7 5 ^{\circ} ) s i n ( 9 0 ^{\circ} - 1 5 ^{\circ} )}{c o s 1 5 ^{\circ} c o s 7 5 ^{\circ}} \frac{c o s 7 5 ^{\circ} c o s 1 5 ^{\circ}}{c o s 1 5 ^{\circ} c o s 7 5 ^{\circ}} 1$