Trigonometric Identities Question 48
Question: $ \sin 12{}^\circ \sin 48{}^\circ \sin 54{}^\circ = $
[IIT 1982; Kerala (Engg.) 2001]
Options:
A) 1/16
B) 1/32
C) 1/8
D) 1/4
Show Answer
Answer:
Correct Answer: C
Solution:
$ \sin ,12^{o},\sin ,48^{o},\sin ,54^{o}=\frac{1}{2},{ \cos 36^{o}-\cos 60^{o} },\cos ,36^{o} $ $ =\frac{1}{2},[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} ],[ \frac{\sqrt{5}+1}{4} ]=\frac{1}{2},[ \frac{\sqrt{5}-1}{4} ],[ \frac{\sqrt{5}+1}{4} ] $ $ =\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8} $ .
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