Question

if sec theta= root 2 then find the value of 1+tan theta+cosec theta/1+cot theta-cosec theta

Answer 1

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Answer 2

Given that
sec theta = _/2
=>theta = 45°.

So,
Let theta be alpha.
$= > \frac{1 + \tan( \alpha ) + \cosec( \alpha ) }{1 + \cot( \alpha ) - \cosec( \alpha ) } \\ = \frac{1 + \tan(45) + \cosec(45) }{1 + \cot(45) - \cosec(45) } \\ = \frac{1 + 1 + \sqrt{2} }{1 + 1 + \sqrt{2} } \\ = \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ = 1.$



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