Question

What is the value of √3 cosec 20°– sec 20° equal to?

Answer 1

Answer:

Answer Solved by “ ITZHEART29” in the attachment..

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Answer 2

SOLUTION✍️

$√3cosec20° \:–\: sec 20°\\\\\frac{√3}{sin20°} \:–\: \frac{1}{cos 20°}\\\\\frac{[√3cos20º \:–\: sin20°] }{ [sin20°cos20°]}\\\\\frac{4 [\frac{√3}{2} cos 20°\: – \:\frac{1}{2 }sin 20°]}{[2sin 20°cos20°]}\\\\\frac{4 [sin 60°cos20°\:–\: cos60°sin20°]}{sin40°}\\\\\frac{4 sin(60° \:–\: 20°)}{sin40°}\\\\\frac{4 \:\cancel{sin 40°}}{\cancel{sin40°}}\\\\4$

FORMULAS USED

$cosecx = \frac{1}{sinx} \\\\secx = \frac{1}{cosx}\\\\\frac{√3}{2} =sin60° \\\\ \frac{1}{2} = cos60° \\\\ 2\: sinx \:cosx = sin2x \\\\sinA\:cosB \:–\: cosA\:sinB = sin(A - B)$

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