Question

cot2x + tanx = cosec2x​

Answer 1

Answer:

=cot(2x)+tan(x)

=cos(2x)/sin(2x)+tan(x)

=1−2sin²(x)/2sin(x)cos(x) +tan(x)

=1/2sin(x)cos(x)−2sin²(x)/2sin(x)cos(x)+tan(x)

=cosec(2x)−sin(x)/cos(x)+tan(x)

=cosec(2x)−tan(x)+tan(x)

=cosec(2x)

Hence proved.

Answer 2

Step-by-step explanation:

cot2x+tanx

= cos2x/sin2x+ sin2x.sinx/sin2x.cosx

= cos(2x-x)/sin2x.cosx [formula applied]*

= cosx/sin2x.cosx

= 1/sin2x

= cosec2x.

note:-* [ cosx.cosy+ sinx.siny]

:- cos [X-Y]

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