Question

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

Answer 1

________________

You Should First Know

________________

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

Answer 2

The correct answer is $\frac{1}{4}$.

Given: The expression = sin 18° sin 42° sin 78° cosec 54°.

To Find: The value of the expression.

Solution:

As know the identity.

Sinx Sin(60-x)Sin(60+x) = $\frac{1}{4}$Sin3x

sin 18° sin 42° sin 78° cosec 54°

Using the identity.

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

= $\frac{1}{4}$Sin(3*18°) cosec54°

= $\frac{1}{4}$ sin54°cosec54°

= $\frac{1}{4}$

Hence, the value of the expression is $\frac{1}{4}$.

#SPJ3