How do you multiply and simplify $(tan y - cot y) (tan y + cot y)$ $(tany-coty)(tany+coty)$ ?

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Answer 1 · 2018-03-28T11:15:39

$(tan y - cot y) (tan y + cot y) \equiv {tan}^{2} y - {cot}^{2} y$ $(tany-coty)(tany+coty) -= tan^2y-cot^2y$

We have an expression,

$E = (tan y - cot y) (tan y + cot y)$ $E = (tany-coty)(tany+coty)$

This is the difference of two squares, thus we can write:

$E = {tan}^{2} y - {cot}^{2} y$ $E = tan^2y-cot^2y$

The issue of "simplify" is somewhat ambiguous - there are many other ways we can write the expression!

How do you multiply and simplify (tany−coty)(tany+coty)(tany-coty)(tany+coty)?