0

HETAV PATEL

Grade 11,

Courses New

Prove that ~16cos24°.cos48°.cos96°.cos168° =1This question is from S.L.Loney Plane trigonometry part -I

Prove that ~16cos24°.cos48°.cos96°.cos168° =1This question is from S.L.Loney Plane trigonometry part -I

Grade:11

3 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
562-2116_Capture.PNG
Siddharth Singh
100 Points
6 years ago
the dipole moment p induced in an atom of neon gas whe an electric field E is applied. , isP = \alpha\varepsilono E P = np = \varepsilono(K –1)E p = \varepsilono (K –1)E / N the volume of 1 m atoms of neon at N.T.P. is 22.4 litres. N = Na / V Hence on calculation p = 2.65 * 10 ^ –36 Cm
Soumendu Majumdar
159 Points
5 years ago
Dear Student,
L.H.S = 4(2cos24^\circ cos96^\circ)(2cos48^{\circ}cos168^{\circ})
= 4(cos120^{\circ}+cos72^{\circ})(cos216^{\circ}+cos120^{\circ})
= 4(-sin30^{\circ}+sin18^{\circ})(-cos36^{\circ}-sin30^{\circ})
Now,
sin 18^{\circ}= (\sqrt5 -1)/4
cos 36^{\circ}= (\sqrt5 +1)/4
so L.H.S = 
4(\sqrt5-3)(-3-\sqrt5)/16
= (9-5)/4
= 1 =R.H.S [Proved]
Hope it helps!
with regards,
Soumendu
P.S-If you have any confusion in understanding the solution, feel free to ask, I’ll be glad to help you!

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More