What is 1/(sec(x)-1)-1/(sec(x)+1) ?

The solution to 1/(sec(x)-1)-1/(sec(x)+1) is 2cot^2(x)

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simplify 1/(sec(x)-1)-1/(sec(x)+1)

simplify

\frac{1}{sec ( x ) - 1} - \frac{1}{sec ( x ) + 1}

2 cot^{2} (x)

Solution steps

\frac{1}{sec ( x ) - 1} - \frac{1}{sec ( x ) + 1}

Join

\frac{1}{sec ( x ) - 1} - \frac{1}{sec ( x ) + 1} : \frac{2}{( sec ( x ) - 1 ) ( sec ( x ) + 1 )}

= \frac{2}{( sec ( x ) - 1 ) ( sec ( x ) + 1 )}

Simplify

(sec (x) - 1) (sec (x) + 1) : tan^{2} (x)

= \frac{2}{tan ^{2} ( x )}

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= 2 cot^{2} (x)

\frac{- 3}{9}

(x^{2} + 2 x y + y^{2}) (x + y)

- 1 \frac{1}{3}

(10 - 7 i) + (6 + 9 i)

(\frac{5}{6} a + \frac{3}{7} b)^{2}

What is 1/(sec(x)-1)-1/(sec(x)+1) ?
The solution to 1/(sec(x)-1)-1/(sec(x)+1) is 2cot^2(x)