Question #0cc73

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Answer 1 · 2017-04-10T14:08:48

$sec^2(x)cot(x) - cot(x) = tan(x)$

$sec (x) = 1/cos (x)$

and,

$cot (x) = cos(x)/sin(x)$

expanding the given function;

$1/cos^2(x) * cos(x)/sin(x) - cos(x)/sin(x)$

$=> 1/(cos(x)*sin(x)) - cos(x)/sin(x)$

Multiplying the numerator and denominator of $cos(x)/sin(x)$ by $cos(x)$ we get the same denominators for both terms.

$=> 1/(cos(x)*sin(x)) - cos^2(x)/(cos(x) *sin(x))$

Then we can simplify further by taking common denominator;

$=> (1- cos^2(x))/(cos(x)*sin(x))$

we know, that $1- cos^2(x) = sin^2(x)$

Therefore, we have

$sin^2(x) / (cos(x)*sin(x))$

$=>sin^(cancel(2))(x)/ (cos(x)*cancel(sin(x)))$

$=> sin(x) / cos(x)$

$=> tan(x)$