Prove that :

$\dfrac{\text{cos A}}{\text{cosec A + 1}} + \dfrac{\text{cos A}}{\text{cosec A - 1}}$ = 2 tan A

For the following frequency distribution, draw an ogive and then use it to estimate the median.

For the same distribution, as given above, draw a histogram and then use it to estimate the mode.

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that :

$\dfrac{a}{b} = \dfrac{\text{cos α - cos β}}{\text{sin β - sin α}}$

Prove that :

$\sqrt{\dfrac{\text{1 + cos A}}{\text{1 - cos A}}} + \sqrt{\dfrac{\text{1 - cos A}}{\text{1 + cos A}}}$ = 2 cosec A