Question

tan A = y/x show that cosec A =√x² +y²/ y​

Answer 1

Step-by-step explanation:

given tan A = y/x

We know that

$tan ( \alpha ) = \frac{perpendicular}{base}$

so we have

Perpendicular = y

and Base = x

using Pythagoras theorem

$hypotenuse = \sqrt{(perendicular)^{2} + (base)^{2} }$

so ,

$hypotenuse = \sqrt{ {y}^{2} + {x}^{2} } = \sqrt{ {x}^{2} + {y}^{2} }$

now we know that

$cosec( \alpha ) = \frac{hypotenuse}{perpendicular}$

so for angle A , we have

$cosec (a) = \frac{ \sqrt{ {x}^{2} + {y}^{2} } }{y}$

proved