Question

Express Cosec a in terms of sec a​

Answer 1

Answer:

what is this question tell

Answer 2

Answer:

$\csc( \alpha ) = \sqrt{\frac{\sec^{2}( \alpha )}{\sec^{2}( \alpha ) - 1}}$

Step-by-step explanation:

$\csc( \alpha ) = \frac{1}{ \sin( \alpha ) }$

$\sec( \alpha ) = \frac{1}{ \cos( \alpha ) }$

we know that ,

${ \sin^{2}( \alpha ) } + \cos^{2}( \alpha ) = 1$

so,

$\frac{1}{ \csc^{2}( \alpha )} + \frac{1}{\sec^{2}( \alpha )} = 1$

$\frac{1}{ \csc^{2}( \alpha )} = 1 - \frac{1}{\sec^{2}( \alpha )}$

$\frac{1}{ \csc^{2}( \alpha )} = \frac{\sec^{2}( \alpha ) - 1}{\sec^{2}( \alpha )}$

${ \csc^{2}( \alpha )} = \frac{\sec^{2}( \alpha )}{\sec^{2}( \alpha ) - 1}$

square root on both sides

$\csc( \alpha ) = \sqrt{\frac{\sec^{2}( \alpha )}{\sec^{2}( \alpha ) - 1}}$