The value of sin 10° ⋅ sin 30° ⋅ sin 50°- sin 70° is

Question

The value of sin 10° ⋅ sin 30° ⋅ sin 50°- sin 70° is (A) (1/8) (B) (3/16) (C) (√3/16) (D) (1/16)

Tardigrade Admin · Accepted Answer

sin 10° ⋅ sin 30° ⋅ sin 50° ⋅ sin 70° =(1/2) ⋅ sin 10° ⋅ (1/2)(2 sin 70° ⋅ sin 50°) =(1/2) sin 10° ⋅ (1/2) cos (70°, 50°). .- cos (70°+50°) =(1/2) sin 10° ⋅ (1/2) cos 20°- cos 120° =(1/2) sin 10° ⋅ (1/2)( cos 10°+(1/2)) =(1/4) sin 10° ⋅ cos 20°+(1/8) sin 10° =(1/4) ⋅ (1/2)( sin 30°- sin 10°)+(1/8) ⋅ sin 10° =(1/8) ⋅ sin 30°-(1/8) sin 10°+1 / 8 sin 10° =(1/8) ⋅ (1/2)-0=(1/16)

Q. The value of $sin 1 0^{\circ} \cdot sin 3 0^{\circ} \cdot sin 5 0^{\circ} - sin 7 0^{\circ}$ is

$\frac{1}{8}$

$\frac{3}{16}$

$\frac{3}{16}$

$\frac{1}{16}$

Q. The value of sin10∘⋅sin30∘⋅sin50∘−sin70∘ is

81​

163​

163​​

161​

Q. The value of $sin 1 0^{\circ} \cdot sin 3 0^{\circ} \cdot sin 5 0^{\circ} - sin 7 0^{\circ}$ is

$\frac{1}{8}$

$\frac{3}{16}$

$\frac{3}{16}$

$\frac{1}{16}$