Question

Show that the value of [cot (π/4 - θ) - 1 ] (cotθ - 1) is independent of θ

Answer 1

Answer:

$(\frac{ \cot( \frac{\pi}{4} ) \cot( \alpha ) + 1 }{ \cot( \alpha ) - \cot( \frac{\pi}{4} ) } - 1)( \cot( \alpha ) - 1) =$

$( \frac{ \cot( \alpha ) + 1}{ \cot( \alpha ) - 1} - 1)( \cot( \alpha ) - 1) =$

$\cot( \alpha ) + 1 - \cot( \alpha ) + 1 = 2$

so proved..