SATHEE: Trigonometrical Ratios and Identities 1 Question 1

Trigonometrical Ratios and Identities 1 Question 1

1. The value of $\sin 10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ}$ is

(a) $\frac{1}{36}$

(b) $\frac{1}{32}$

(d) $\frac{1}{18}$

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Answer:

Correct Answer: 1. (c)

Solution:

We have, $\sin 10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ}$ $= \sin (30^{\circ}) [\sin (10^{\circ}) \sin (50^{\circ}) \sin (70^{\circ})]$

$\begin{aligned} = \frac{1}{2} [\sin (10^{\circ}) \sin (60^{\circ} - 10^{\circ}) \sin (60^{\circ} + 10^{\circ})] \\ = \frac{1}{2} \frac{1}{4} \sin (3 (10^{\circ})) \end{aligned}$

$[∵ \sin θ \sin (60^{\circ} - θ) \sin (60^{\circ} + θ) = \frac{1}{4} \sin 3 θ]$

$= \frac{1}{8} \sin 30^{\circ} = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$

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Trigonometrical Ratios and Identities 1 Question 1

1. The value of sin⁡10∘sin⁡30∘sin⁡50∘sin⁡70∘ is

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1. The value of $\sin 10^{\circ} \sin 30^{\circ} \sin 50^{\circ} \sin 70^{\circ}$ is