Question

tanx + cotx = 2cosec 2x​

Answer 1

Answer:

taking L.H.S

tanx+cotx

we know tanx=sinx/cosx

and cotx=cosx/sinx

now tanx+cotx

=sinx/cosx+cosx/sinx

then taking L.C.M

=sin^2 x +cos^2 x/sinxcosx

we know Sin^2x+Cos^2x=1

=1/sinxcosx

multiply and divide by 2

=2/2sinxcosx

=2/sin2x

=2cosec2x

Hence proved

formulas used in this question are sin2x=2sinxcosx

cosec2x=1/sin2x

Answer 2

Answer:

$\tan(x) + \cot(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } \\ = \frac{sin^{2} x + {cos}^{2}x }{sinx \:. cosx} \\ = \frac{1}{sinx \:. cosx} \\ = \frac{2}{2sinx \:. cosx} \\ = \frac{2}{sin2x} \\ = 2 \csc(2x) \\ hence \: proved$