Question

Express trigonometric sec theta in terms of cosec theta

Answer 1

Answer:

let theta be a.

sec(90°-a)=cosec a

or

sec a =√(1/cos^2 a)

= √(1/1-sin^2a)

=√(1/1-1/cosec^2a)

Answer 2

The required expression is $\sec\theta = \frac{\csc\theta}{\sqrt{\csc^2\theta-1}}$.

Step-by-step explanation:

Consider the provided information.

Express trigonometric sec θin terms of cosecθ.

$\sec\theta = \frac{1}{\cos\theta}$

$\sec^2\theta = \frac{1}{\cos^2\theta}$

$\sec^2\theta = \frac{1}{1-\sin^2\theta}$

$\sec^2\theta = \frac{1}{1-\frac{1}{\csc^2\theta}}$

$\sec^2\theta = \frac{\csc^2\theta}{\csc^2\theta-1}$

$\sec\theta = \frac{\csc\theta}{\sqrt{\csc^2\theta-1}}$

Hence, the required expression is $\sec\theta = \frac{\csc\theta}{\sqrt{\csc^2\theta-1}}$.

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