Question

if tan theta= 1 / root 3, then evaluate cosec squared theta- sec squared theta / cosec square theta + sec square theta

Answer 1

HOPE IT HELPS YOU.....

Answer 2

Answer:-

$\frac{1}{2}$

Step-by-step explanation:

Hey mate

Solution :-

It is given that

$tan \: theta \: = \frac{1}{ \sqrt{3} }$

So we can two side

That is Ab =root 3 and bc =1

Now we can find third side

By using Pythagoras theorem

${ac}^{2} = {ab}^{2} + {bc}^{2}$

${ac}^{2} = {( \sqrt{3} )}^{2} + {1}^{2}$

${ac}^{2} = 4 \\ {ac} = 2$

$now \: we \: have \: \: trigonometric \: ratio$

$\sec( theta) = \frac{hypotenuse}{base} \\ \\ \csc(theta) = \frac{hypotenuse}{opposite }$

By using we can evaluate

And we get the vaule

That is

$\frac{1}{2}$