Question

sin 18° sin 42° sin 78° cosec 54°​find value​

Answer 1

Answer:

sin18 sin(60-18) sin(60+18) cosec54

$\frac{1}{4} sin \: 54 \times \frac{1}{sin54}$

since sinx*sin(60-x)*sin(60+x) = 1/4 sinx

and cosec x = 1/sinx

= 1/4

hope it helps you.....!

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Answer 2

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You Should First Know

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1. $cosec(x) \: = \frac{1}{ \sin(x) }$

2. $\sin(60) \times \sin(60 - 18) \times \sin(60 + 18) = \\ \frac{1}{4} \sin(54)$

$\huge \red{ \boxed{ \bf{ \ulcorner{ \mid{ \overline{ \underline{ANSWER}}}}}\mid }}$

$= > \sin(18) \sin(42) \sin(78) cosec(54) \\ = > \frac{1}{4} \times \sin(54) \times cosec(54) \\ = > \frac{1}{4} \times \sin(54) \times \frac{1}{\sin(54) } \\ = > \frac{1}{4}$

Hope It Helps