Pertanyaan

Tentukan hasil dari 4 sin ( 30 5 ∘ + x ) − 6 cos ( 21 5 ∘ + x ) 5 sin ( 12 5 ∘ + x ) + 4 cos ( 14 5 ∘ − x ) = …

Tentukan hasil dari $\frac{5 sin ( 12 5 ^{\circ} + x ) + 4 cos ( 14 5 ^{\circ} - x )}{4 sin ( 30 5 ^{\circ} + x ) - 6 cos ( 21 5 ^{\circ} + x )} = \dots$

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Habis dalam

Klaim

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari 4 sin ( 30 5 ∘ + x ) − 6 cos ( 21 5 ∘ + x ) 5 sin ( 12 5 ∘ + x ) + 4 cos ( 14 5 ∘ − x ) adalah 2 1 .

hasil dari

\frac{5 sin ( 12 5 ^{\circ} + x ) + 4 cos ( 14 5 ^{\circ} - x )}{4 sin ( 30 5 ^{\circ} + x ) - 6 cos ( 21 5 ^{\circ} + x )}

adalah

\frac{1}{2}

Pembahasan

Ingat aturan pada sudut berelasi! sin ( 9 0 ∘ + x ) sin ( 27 0 ∘ + x ) cos ( 18 0 ∘ − x ) cos ( 18 0 ∘ + x ) = = = = cos x − cos x − cos x − cos x Maka, = = = = = 4 s i n ( 30 5 ∘ + x ) − 6 c o s ( 21 5 ∘ + x ) 5 s i n ( 12 5 ∘ + x ) + 4 c o s ( 14 5 ∘ − x ) 4 s i n ( 27 0 ∘ + 3 5 ∘ + x ) − 6 c o s ( 18 0 ∘ + 3 5 ∘ + x ) 5 s i n ( 9 0 ∘ + 3 5 ∘ + x ) + 4 c o s ( 18 0 ∘ − 3 5 ∘ − x ) 4 s i n ( 27 0 ∘ + ( 3 5 ∘ + x )) − 6 c o s ( 18 0 ∘ + ( 3 5 ∘ + x )) 5 s i n ( 9 0 ∘ + ( 3 5 ∘ + x )) + 4 c o s ( 18 0 ∘ − ( 3 5 ∘ + x )) − 4 c o s ( 3 5 ∘ + x ) + 6 c o s ( 3 5 ∘ + x ) 5 c o s ( 3 5 ∘ + x ) − 4 c o s ( 3 5 ∘ + x ) 2 c o s ( 3 5 ∘ + x ) c o s ( 3 5 ∘ + x ) 2 1 Jadi, hasil dari 4 sin ( 30 5 ∘ + x ) − 6 cos ( 21 5 ∘ + x ) 5 sin ( 12 5 ∘ + x ) + 4 cos ( 14 5 ∘ − x ) adalah 2 1 .

Ingat aturan pada sudut berelasi!

$sin (9 0^{\circ} + x) sin (27 0^{\circ} + x) cos (18 0^{\circ} - x) cos (18 0^{\circ} + x) = = = = cos x - cos x - cos x - cos x$

Maka,

$= = = = = \frac{5 s i n ( 12 5 ^{\circ} + x ) + 4 c o s ( 14 5 ^{\circ} - x )}{4 s i n ( 30 5 ^{\circ} + x ) - 6 c o s ( 21 5 ^{\circ} + x )} \frac{5 s i n ( 9 0 ^{\circ} + 3 5 ^{\circ} + x ) + 4 c o s ( 18 0 ^{\circ} - 3 5 ^{\circ} - x )}{4 s i n ( 27 0 ^{\circ} + 3 5 ^{\circ} + x ) - 6 c o s ( 18 0 ^{\circ} + 3 5 ^{\circ} + x )} \frac{5 s i n ( 9 0 ^{\circ} + ( 3 5 ^{\circ} + x )) + 4 c o s ( 18 0 ^{\circ} - ( 3 5 ^{\circ} + x ))}{4 s i n ( 27 0 ^{\circ} + ( 3 5 ^{\circ} + x )) - 6 c o s ( 18 0 ^{\circ} + ( 3 5 ^{\circ} + x ))} \frac{5 c o s ( 3 5 ^{\circ} + x ) - 4 c o s ( 3 5 ^{\circ} + x )}{- 4 c o s ( 3 5 ^{\circ} + x ) + 6 c o s ( 3 5 ^{\circ} + x )} \frac{c o s ( 3 5 ^{\circ} + x )}{2 c o s ( 3 5 ^{\circ} + x )} \frac{1}{2}$

Jadi, hasil dari $\frac{5 sin ( 12 5 ^{\circ} + x ) + 4 cos ( 14 5 ^{\circ} - x )}{4 sin ( 30 5 ^{\circ} + x ) - 6 cos ( 21 5 ^{\circ} + x )}$ adalah $\frac{1}{2}$ .