The value of 3 c o s e c 20 ° - sec 20 ° cos 20 ° cos 40 ° cos 60 ° cos 80 ° is equal to: [2026]

Question

The value of $\frac{\sqrt{3} c o s e c 20 ° - \sec 20 °}{\cos 20 ° \cos 40 ° \cos 60 ° \cos 80 °}$ is equal to: [2026]

Smart Achievers · Accepted Answer

(1)

$E = \frac{\frac{\sqrt{3}}{\sin 20 °} - \frac{1}{\cos 20 °}}{\frac{1}{2} \cdot \frac{1}{4} \cdot \cos 60 °}$

$= \frac{\sqrt{3} \cos 20 ° - \sin 20 °}{\cos 20 ° . \sin 20 °} \cdot 16$

$= \frac{(\frac{\sqrt{3}}{2} \cos 20 ° - \frac{1}{2} \sin 20 °) 32 \times 2}{2 \cos 20 ° . \sin 20 °}$

$= \frac{\sin 40 °}{\sin 40 °} \times 64 = 64$

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