Question

express sec teeta in terms of cosec teeta​

Answer 1

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

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

$\huge\rm sec\theta = \frac{1}{\sqrt{1 - \frac{1}{cosec^2\theta}}}$

$\huge\rm sec\theta = \frac{1}{\sqrt{ \frac{cosec^2\theta - 1}{cosec^2\theta}}}$

$\huge\rm sec\theta = \frac{cosec\theta}{\sqrt{cosec^2\theta - 1}}$

Answer 2

( I am using 'x' in place of θ )

We know that

    Sin²x + Cos²x = 1

    Cosx =$\sqrt{1-Sin^{2}x }$

    Cosx = $\sqrt{1-\frac{1}{Cosec^{2}x } }$   .........( since sinx = $\frac{1}{cosecx}$ )

Secx =  $\frac{1}{Cosx}$

       

Secx = $\frac{1}{\sqrt{1-\frac{1}{cosec^{2}x } } }$

Secx = $\frac{Cosecx}{\sqrt{cosec^{2}x - 1 } }$

HOPE IT HELPS !!