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Grade 11Trigonometry

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

Profile image of Ayush Baghel
8 Years agoGrade 11
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3 Answers

Profile image of Deepak Kumar Shringi
8 Years ago
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Profile image of Siddharth Singh
8 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
Profile image of Soumendu Majumdar
8 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!

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