Question

√1+cos theta /√1-Cos theta is equal to​

Answer 1

Question:-

$\sf \large \sqrt{ \frac{1 + cos \theta}{1 - cos \theta} } \: is \: equal \: to$

Options:

(a) sec θ + tan θ.

(b) – cosec θ + cot θ.

(c) cosec θ – cot θ.

(d) cosec θ + cot θ.

Given:-

$\sf \large \sqrt{ \frac{1 + cos \theta}{1 - cos \theta} }.$

To Find:-

$\sf \large \sqrt{ \frac{1 + cos \theta}{1 - cos \theta} } = \sf ?$

Solution:-

On rationalising:

$\sf \large \sqrt{ \frac{1 + cos \theta}{1 - cos \theta} } = \sqrt{ \frac{(1 + cos \theta) {}^{2} }{1 - cos {}^{2} \theta } }$

$\sf \large = \sqrt{ \frac{(1 + cos \theta) {}^{2} }{sin {}^{2} \theta } } = \frac{1 + cos \theta}{sin \theta}$

$\sf \large = \frac{1}{sin \theta} + \frac{cos \theta}{sin \theta} = cosec \theta + cot \theta.$

Answer:-

${ \boxed { \sf \large \green{ \sf \large \sqrt{ \frac{1 + cos \theta}{1 - cos \theta} } = cosec \theta + cot \theta.}}}$

Hope you have satisfied. ⚘

Answer 2

Square root of 1 + cos theta by 1 - cos theta is equal to cosec theta + cot theta.

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