Question #fda82

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Answer 1 · 2017-10-07T16:40:11

#tan(x) +cot (x) = 1/(cos(x)*sin(x))= 1/(0.5(sin(2x)))=2"cosec"(2x)#

#tan(x) + cot(x) = sin(x)/cos(x) + cos(x)/sin(x)#

Cross multiply to get

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

Using the trigonometric identity

#sin^2(x) + cos^2(x) = 1#

and

#sin(2x) = 2cos(x)sin(x)#

we can rewrite the equation like this:

#(sin^2(x) + cos^2(x))/(sin(x)cos(x)) = 1/(1/2*sin(2x))#

Which is the same as #2"cosec"(2x)#