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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