SATHEE: Trigonometrical Ratios and Identities 1 Question 23

Trigonometrical Ratios and Identities 1 Question 23

23. If $k = \sin \frac{π}{18} \sin \frac{5 π}{18} \sin \frac{7 π}{18}$ , then the numerical value of $k$ is

$(1993, 2 M)$

Show Answer

Solution:

Using the relation,

$\sin θ \sin \frac{π}{3} - θ \sin \frac{π}{3} + θ = \frac{\sin 3 θ}{4}$

Taking $θ = \frac{π}{18}$ , we get

$\sin \frac{π}{18} \cdot \sin \frac{5 π}{18} \cdot \sin \frac{7 π}{18} = \frac{\sin \frac{π}{6}}{4} = \frac{1}{8}$

Alternative Method

Given, $k = \sin 10^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$

$= \cos 80^{\circ} \cdot \cos 40^{\circ} \cdot \cos 20^{\circ}$

$= \cos A \cdot \cos 2 A \cdot \cos 2^{2} A = \frac{\sin 2^{3} A}{2^{3} \sin A}$

where, $A = 20^{\circ}$

$= \frac{\sin 160^{\circ}}{8 \sin 20^{\circ}} = \frac{\sin (180^{\circ} - 20^{\circ})}{8 \sin 20^{\circ}} = \frac{\sin 20^{\circ}}{8 \sin 20^{\circ}} = \frac{1}{8}$

पिछला

अगला

गोपनीयता नीति

द्वारा संचालित Prutor@IITK

sathee@iitk.ac.in

SATHEE का मीडिया कवरेज

खेल स्टोर

ऐप स्टोर

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Trigonometrical Ratios and Identities 1 Question 23

23. If k=sin⁡π18sin⁡5π18sin⁡7π18, then the numerical value of k is

Solution:

Alternative Method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

23. If $k = \sin \frac{π}{18} \sin \frac{5 π}{18} \sin \frac{7 π}{18}$ , then the numerical value of $k$ is