Question

Prove the following:

2cosec 2x + cosec x = `secx cot(x/2)`

Answer 1

L.H.S. = 2cosec 2x + cosec x

= `2/(sin2x) + 1/sinx`

= `2/(2sin x cosx) + 1/sinx`

= `1/(sinx cosx) + 1/sinx`

= `(1 + cosx)/(sinx cosx)`

= `(2cos^2(x/2))/([2sin(x/2)cos(x/2)]cosx`

= `1/cosx * (cos(x/2))/(sin(x/2)`

= `sec x cot (x/2)`

= R.H.S.