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 $2"cosec"(2x)$