Evaluate sec((3pi)/4)^2-1

$\sec^{2} (\frac{3 π}{4}) - 1$

Step 1

Apply pythagorean identity.

$\tan^{2} (\frac{3 π}{4})$

Step 2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

${(- \tan (\frac{π}{4}))}^{2}$

Step 3

The exact value of $\tan (\frac{π}{4})$ is $1$ .

${(- 1 \cdot 1)}^{2}$

Step 4

Multiply $- 1$ by $1$ .

${(- 1)}^{2}$

Step 5

Raise $- 1$ to the power of $2$ .

$1$

Evaluate sec((3pi)/4)^2-1

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