यदि `"cosec" theta - cot theta = 1/(sqrt(3))` जहाँ ` theta !=` है , तो` cos theta` का मान क्या है ?

Options

A. `0`
B. `(sqrt(3))/2`
C. `1/2`
D. `1/(sqrt(2))`

Answer

C

Explanation

दिया है , `"cosec" theta - cot theta = 1/(sqrt(3))`
[ जहाँ `theta, != 0 ` ]
` rArr 1/(sin theta ) - (costheta )/(sin theta) = 1/(sqrt(3))`
` rArr ((1-cos theta ))/(sin theta ) = 1/(sqrt(3))`
` rArr (2 sin ^(2) theta//2)/(2 sin theta //2 xx cos theta //2)= 1/(sqrt(3))`
` rArr tan. theta /2 = tan 30^(@)`
` rArr theta/2 = 30^(@)`
` rArr theta = 60^(@)`
` :. cos 60^(@) = 1/2 `