Question

find cosec 30 degree and cos 60 degree geometrically.

Answer 1

cosec 30° = 1/ sin 30° = 1/ (1/2) = 2
cos 60° = sin (90-60) = sine 30° = 1/2

Answer 2

Consider a triangle with each side equal to 2a.

<A=<B=<C=60°

Draw AD perpendicular to BC.

∆BDA~=~∆CDA by RHS.

So, BD= CD

and, <BAD=<CAD =30° by CPCT.

By Pythagoras theorem,

AD=√3a

In ∆BDA,

cosec 30°=AB/BD =2a/a =2

and, cos 60°=BD/AB=a/2a=1/2