Question

Prove that √3 cosec 20° - sec 20° = 4

Answer 1

Answer:

4

Step-by-step explanation:

Formula used:

1.sin(A-B)= sinA cosB - cosA sinB

2. sin2A = 2 sinA cosA

$\sqrt{3}\:cosec20-sec20$

$=\sqrt{3}\:(\frac{1}{sin20})-(\frac{1}{cos20})$

$=2[\frac{\sqrt{3}}{2}\:(\frac{1}{sin20})-\frac{1}{2}(\frac{1}{cos20})]$

$=\frac{2[sin60\:cos20-cos60\:sin20]}{sin20\:cos20}$

$Multiply\:Nr.\:and\:Dr.by2$

$=\frac{4[sin(60-20)]}{2sin20\:cos20}$

$=\frac{4[sin40]}{sin40}$

$= 4$