Question

If cosec A=2 then find the value of 1/tanA +sin A/ 1+cos A

Answer 1

Hey!!

Given,

CosecA = 2 = 2 / 1 = H / P

Here H ( Hypotenuse ) = 2 , P ( Perpendicular ) = 1 , B ( Base ) = ?

By pythagoras theorem

$b = \sqrt{h {}^{2} - p {}^{2} } \\ \\ = > \sqrt{2 {}^{2} - 1 {}^{2} } \\ \\ = > \sqrt{4 - 1} \\ \\ = > \sqrt{3} .$

=> 3.

b = 3

Here tanA = P / B = 1 / 3

sinA = P / H = 1 / 2

cosA = B / H = 3 / 1 = 3

1/tanA +sin A/ 1+cos A

=> 1 / 1 / 3 + 1/ 2 + 1 / 3

=> 3 + 1/ 2 + 1 / 3

=> 4 + 3 + 2 / 6

=> 14 / 6

=> 7 / 3.

Hope it helps! !