Question

Find the value of (1/tanθ) + (sinθ/(1 + cosθ)), if 1 + cot^2θ = (√(3 + 2√2) - 1)^2.

Answer 1

We have,

$= > \frac{1}{ \tan( \theta) } + \frac{ \sin( \theta) }{1 + \cos( \theta) } \\ = > \frac{ \cos( \theta) }{ \sin( \theta) } + \frac{1 - \cos( \theta) }{ \sin( \theta) } \\ = > \csc( \theta)$

Since,

$= > 1 + \cot^{2} ( \theta) = \: \csc^{2} ( \theta) = ( \sqrt{3 + 2 \sqrt{2} } - 1)^{2} \\ \\ = > \csc( \theta) = \sqrt{3 + 2 \sqrt{2} } - 1$