Question

prove that under root cosec theta+ 1/cosec theta- 1 = cos theta/1- sin theta

Answer 1

hope so it helps you....

Answer 2

To prove :

$\sqrt{\frac{\csc\theta+1}{\csc\theta-1}}= \frac{\cos\theta}{1-\sin\theta}$

Step-by-step explanation:

$\sqrt{\frac{\csc\theta+1}{\csc\theta-1}}\\\\rationalising \\\\\sqrt{\frac{\csc\theta+1}{\csc\theta-1}\times \frac{\csc\theta+1}{\csc\theta+1}}\\\\\sqrt{\frac{(\csc\theta+1)^2}{cot^2\theta}}\\\\\frac{\csc\theta+1}{\cot \theta}\\\\\frac{\frac{1}{\sin\theta}+1}{\cot\theta}\\\\\text{taking lcm}\\\\\frac{\frac{1+\sin\theta}{\sin\theta}}{\frac{\cos\theta}{\sin\theta}}$

$\\\\\frac{1+\sin\theta}{\cos\theta}\\\\\frac{(1+\sin\theta)(1-\sin\theta)}{\cos\theta(1-\sin\theta)}\\\\\frac{1-\sin^2\theta}{\cos\theta(1-\sin\theta)}\\\\\frac{\cos^2\theta}{\cos\theta(1-\sin\theta)}\\\\\frac{\cos\theta}{1-\sin\theta}$

hence proved

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