Question

express cosec theta in terms of tan theta

Answer 1

Answer:

Step-by-step explanation:

$cosec\space\theta\spac in term of tan\space\theta :-$

$cosec\space\theta = \frac{1}{sin\space\theta}$

Before we change cosec theta in term of tan theta, First we have to change sin theta in term of tan theta : -

$\frac{ sin\space\theta}{cos\space\theta} = tan\space\theta \\\\sin\space\theta = tan\space\theta\space\cdot\space cos\space\theta \\\\cos\space\theta = \frac{1}{sec\space\theta}$

From the Above Equation We get : --

$sin\space\theta = tan\space\theta\space\cdot\space\frac{1}{sec\space\theta} \\\\sec^2\space\theta = tan^2\space\theta+1 \\\\sec\space\theta = \sqrt{tan^2\space\theta+1}$

From the Above Equation We get : --

$sin\space\theta = tan\space\theta\space\cdot\space\frac{1}{\sqrt{tan^2\space\theta+1}}\\\\sin\space\theta = \frac{tan\space\theta\space}{\sqrt{tan^2\space\theta+1}}$

From the Above Equation We get sin theta in term of tan theta , So That :--

$cosec\space\theta = \frac{1}{sin\space\theta}\\\\cosec\space\theta = \frac{1}{\frac{tan\space\theta\space}{\sqrt{tan^2\space\theta+1}}}\\\\\\\left[\therefore cosec\space\theta = \frac{\sqrt{tan^2\space\theta+1}}{tan\space\theta\space}\right]$

And For your Useful , I have Attached A Pdf , In that the answer is  explained Clearly:

d679d5e6f8c2e0136b2013d86a2494ce.pdf

Answer 2

Answer:

cosec theta = tan / ✓1+ tan ² theta