Question

Solve the equation: cot x + cosec x = √3

Answer 1

cot 37.197.....+cosec*(1.147.....*1.147....=root 3

Answer 2

Answer:

$x=\frac{\pi }{3}$

Step-by-step explanation:

As we know that

cot x= cos x/sin x

cosec x=1/sin x

$\frac{cos\:x}{sin\:x} +\frac{1}{sin\:x} =\sqrt{3}\\\\ \frac{cos\:x+1}{sin\:x} =\sqrt{3}\\\\ \frac{2cos^{2}\frac{x}{2} }{2cos\frac{x}{2}sin\frac{x}{2}} =\sqrt{3} \\\\ \frac{cos\frac{x}{2} }{sin\frac{x}{2} }=\sqrt{3}\\ \\ cot\frac{x}{2}=\sqrt{3}$

$\frac{x}{2} =cot^{-1}\sqrt{3} \\\\\frac{x}{2} =cot^{-1}cos\frac{\pi}{6}\\\\\\\frac{x}{2}=\frac{\pi }{6} \\\\\\x=\frac{2\pi }{6}\\\\\\x =\frac{\pi }{3}$

Hope it helps you.