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Maths-

General

Easy

Question

$sin space 20 to the power of ring operator open parentheses 4 plus sec space 20 to the power of ring operator close parentheses$ =

$\frac{1}{2}$
$\sqrt{2}$
$\sqrt{3}$
1

hint Hint:

In this question, we have to find the value of the given equation. For that we will simplify the given equation by converting them to sine and cosine and later simplify it using some trigonometric identity to find the required value.

The correct answer is: $square root of 3$

$space space space space space sin space 20 to the power of ring operator open parentheses 4 plus sec space 20 to the power of ring operator close parentheses equals 4 sin space 20 degree plus fraction numerator sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 4 sin 20 degree. cos 20 degree plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 2 left parenthesis 2 sin space 20 degree. cos space 20 degree right parenthesis plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 2 sin space 40 degree plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 2 sin space left parenthesis 60 minus 20 right parenthesis degree plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 2 open parentheses sin space 60 degree cos space 20 degree minus cos space 60 degree sin space 20 degree close parentheses plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator 2 open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style cos space 20 degree minus begin display style 1 half end style sin space 20 degree close parentheses plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator square root of 3 cos space 20 degree minus sin space 20 degree plus sin space 20 degree over denominator cos space 20 degree end fraction equals fraction numerator square root of 3 cos space 20 degree over denominator cos space 20 degree end fraction equals square root of 3$

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