यदि `tan A - tan B=x` एवं ` cot B - cot A = y ,` तब ` cot (A-B) ` का मान क्या है ?

Options

A. ` 1/y-1/x`
B. ` 1/x-1/y`
C. ` 1/x+1/y`
D. ` -1/x-1/y`

Answer

c

Explanation

दिया है , `tan A - tan B = x `
तथा ` cut B - cot A = y`
` rArr = ( sin A * cos B - sin B * cos A)/( cos A * cos B) `
` = ( sin ( A-B))/(cos A * cos B) rArr 1/x = ( cosA* cosB)/(sin (A-B))`
तथा ` y = ( cos * B * sin A - cos A * cos B )/( sin A * sin B)`
` = ( sin (A-B))/(sin A * sin B)`
` rArr 1/y = ( sin A* sin B)/(sin (A -B))`
` :. 1/x + 1/y = ( cos A* cos B + sin A * sin B)/(sin (A-B))`
` rArr 1/x + 1/y = cos (A - B)/(sin (A-B))`
` rArr cot (A - B) = 1//x + 1//y`