यदि ` sec A = 2` तो , `(1)/(cot A) + (cos A)/(1 + sin A)` का मान ज्ञात कीजिए |

Options

A. `52`
B. `12`
C. `9`
D. `2`

Answer

D

Explanation

दिया है : `sec A = 2 = (2)/(1)`
एक समकोण त्रिभुज बनाते है जिसमे
` angle ABC = 90^(@) , AB = k ` और AC = 2k

`Delta ABC ` में
पाइथागोरस प्रमेय से
` AB^(2) + BC^(2) = AC^(2)`
` rArr BC^(2) = AC^(2) - AB^(2) = (2k)^(2) - (k)^(2) = 4k^(2) - k^(2) = 3k^(2)`
`rArr BC = sqrt(3k)`
अब ` cos A = (AB)/(BC) = (k)/(sqrt(3)k) /(2k) = (sqrt(3))/(2)` और ` cos A = (AB)/(AC) = (k)/(2k) = (1)/(2)`
` therefore (1)/(cotA) + (cos A)/(1 + sin A) = (1)/(1/(sqrt(3)) )+ ((1)/(1))/((sqrt(3))/(2)) = sqrt(3) + ((1)/(2))/((2+sqrt(3))/(2))`
` sqrt(3) + (1xx(2-sqrt(3)))/((2+sqrt(3))(2-sqrt(3))) = sqrt(3) + (2-sqrt(3))/(4 -3)`
` sqrt(3) + 2 - sqrt(3) = 2 `