How do you simplify the expression $(tant)/(tant+cott)$ ?

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Answer 1 · 2016-10-15T14:14:37

This expression can be simplified to $sin^2t$ .

For this problem, the following identities will be important:

$•tantheta = sintheta/costheta$

$•cot theta = 1/tantheta= 1/(sintheta/costheta) = costheta/sintheta$

Start simplifying:

$=(sint/cost)/(sint/cost + cost/sint)$

$= (sint/cost)/((sin^2t + cos^2t)/(costsint))$

We can now apply the identity $sin^2alpha + cos^2alpha = 1$ to the numerator of the lower expression.

$=(sint/cost)/(1/(costsint))$

$=sint/cost xx (costsint)$

$= sint xx sint$

$= sin^2t$

Hopefully this helps!

How do you simplify the expression (tant)/(tant+cott)(tant)/(tant+cott)?