Trigonometry Examples

$\tan^{4} (t) - \sec^{4} (t) = 1 - 2 \sec^{2} (t)$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $1$ from both sides of the equation.

$\tan^{4} (t) - \sec^{4} (t) - 1 = - 2 \sec^{2} (t)$

Step 1.2

Add $2 \sec^{2} (t)$ to both sides of the equation.

$\tan^{4} (t) - \sec^{4} (t) - 1 + 2 \sec^{2} (t) = 0$

Step 2

Set the argument in $\tan (t)$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

$t = \frac{π}{2} + π n$ , for any integer $n$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${t | t = \frac{π}{2} + π n}$ $n$ , for any integer $n$

Step 4