tg(x) + ctg(x) = 2cosec (2x)

We know that tg(x) = sin(x) /cos(x)

and ctg(x)= cos(x) /sin(x)

Now let us substitute:

sin(x)/cos(x) + cos(x)/sin(x)

Now we need to determine the common denominator:

sin^2 (x) + cos^2(x) / sinxcosx

But we know that sin^2 x+ cos^2 x=1

==> 1/ sinxcosx

Multiply and divide by 2:

==> 2/2sinxcosx

Now 2sinx cosx = sin2x

==> 2/ sin2x

But cosec x= 1/sinx

==> 2/2sin2x = 2 cosec 2x

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