Verify cos x (cot x+ tan x) = csc x?

Answer 1

cosxcotx + cosxtanx (multiplied out)
=cosx (cosx/sinx) + cosx (sinx/cosx)
=( (cosx)^2/sinx ) + sinx
=(1 - (sinx)^2/sinx ) + sinx (p.s look at proof)
=(1/sinx) - ( ((sinx)^2)/sinx ) + sinx
=1/sinx = cscx

proof of change of (cosx)^2
(cosx)^2 + (sinx)^2 = 1
(cosx)^2 = 1 - (sinx)^2

hope that helped

Answer 2

cos x [ cos x / sin x + sin x / cos x ]
cos ² / sin x + sin x
( cos ² x + sin ² x ) / sin x
1 / sin x
cosec x