The expression sin 27 ° cos ⁡ 57 ° sin ⁡ 87 ° simplifies to

Question

The expression sin 27 ° cos ⁡ 57 ° sin ⁡ 87 ° simplifies to (A) (sin 9 ° /4) (B) (cos 9 ° /4) (C) (sin 9 ° /2) (D) (cos 9 ° /2)

Tardigrade Admin · Accepted Answer

sin 27 ° cos â¡ 57 ° sin â¡ (90 ° - 3 ° ) =(1/2)sin 27 ° (2 cos â¡ 57 ° cos â¡ 3 ° ) =(1/2)sin 27 ° (cos â¡ 60 ° + cos â¡ 54 ° ) =(1/2)sin 27° ((1/2))+(1/2)sinâ¡27° sinâ¡36° =(1/4)sin 27 ° + (1/4) (2 sin â¡ 27 ° sin â¡ 36 ° ) =(1/4)sin 27 ° + (1/4) (cos â¡ 9 ° - cos â¡ 63 ° ) =(1/4)sin 27 ° + (1/4) cos â¡ 9 ° -(1/4)sin â¡ 27 ° =(1/4)cos 9 °

Q. The expression $s in 2 7^{\circ} cos 5 7^{\circ} s in 8 7^{\circ}$ simplifies to

$\frac{s in 9 ^{\circ}}{4}$

$\frac{cos 9 ^{\circ}}{4}$

$\frac{s in 9 ^{\circ}}{2}$

$\frac{cos 9 ^{\circ}}{2}$

Q. The expression sin27∘cos⁡57∘sin⁡87∘ simplifies to

4sin9∘​

4cos9∘​

2sin9∘​

2cos9∘​

Q. The expression $s in 2 7^{\circ} cos 5 7^{\circ} s in 8 7^{\circ}$ simplifies to

$\frac{s in 9 ^{\circ}}{4}$

$\frac{cos 9 ^{\circ}}{4}$

$\frac{s in 9 ^{\circ}}{2}$

$\frac{cos 9 ^{\circ}}{2}$