20^ 40^ 60^ 80^ = - Vidyadip

MCQ

$\sin 20^{\circ} \sin 40^{\circ} \sin 60^{\circ} \sin 80^{\circ}=$

A
$\frac{-3}{16}$
B
$\frac{5}{16}$
✓
$\frac{3}{16}$
D
$\frac{-5}{16}$

✓

Answer

Correct option: C.

$\frac{3}{16}$

(C)
$\sin 20^{\circ} \sin 40^{\circ} \sin 60^{\circ} \sin 80^{\circ}$
$=\frac{\sqrt{3}}{2} \sin 20^{\circ} \sin \left(60^{\circ}-20^{\circ}\right) \sin \left(60^{\circ}+20^{\circ}\right)$
$\sin \theta \sin \left(60^{\circ}-\theta\right) \sin \left(60^{\circ}+\theta\right)=\frac{1}{4} \sin 3 \theta$
$=\frac{\sqrt{3}}{2} \cdot \frac{1}{4} \sin 60^{\circ}$
$=\frac{\sqrt{3}}{8} \cdot \frac{\sqrt{3}}{2}$
$=\frac{3}{16}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then

The value of $\lim _{x \rightarrow 2 a} \frac{\sqrt{x-2 a}+\sqrt{x}-\sqrt{2 a}}{\sqrt{x^2-4 a^2}}$ is

The equation of the circle drawn with the two foci of $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ end $-$ point of a diameter is

At $3 : 40,$ the hour and minute hands of a clock are inclined at :

Equation of tangent to the circle $x^2+y^2=10$ at the point with abscissa 1 is

The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is

If the centre, one of the foci and semi-major axis of an ellipse be (0 ,0),(0 ,3) and 5 , then its equation

The probabilities of a student getting first class or second class or third class in an examination are $\frac{2}{7}, \frac{3}{5}, \frac{1}{10}$ respectively. The probability that the student fails is

If $|z|=5$ and $w=\frac{z-5}{z+5}$, then $\operatorname{Re}(w)$ is equation to

The corners are of regular tetrahedrons numbered 1, 2, 3, 4. Three tetrahedrons are tossed. The probability that the sum of upward corners will be 5 is