What is the value of sec^2(-pi/4)-1 ?

The value of sec^2(-pi/4)-1 is 1

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sec^2(-pi/4)-1

sec^{2} (- \frac{π}{4}) - 1

1

Solution steps

sec^{2} (- \frac{π}{4}) - 1

Rewrite using trig identities:

sec (- \frac{π}{4}) = 2

sec (- \frac{π}{4})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{4}) = sec (\frac{π}{4})

= sec (\frac{π}{4})

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= 2

= (2)^{2} - 1

Simplify

(2)^{2} - 1 : 1

(2)^{2} - 1

(2)^{2} = 2

(2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

= 2 - 1

Subtract the numbers:

2 - 1 = 1

= 1

= 1

cot (arcsin (\frac{1}{3}))

15 cos (4 0^{\circ})

arcsin (sin (- \frac{π}{2}))

arctan (\frac{7.4}{14})

\frac{7 sin ( 5 3 ^{\circ} )}{sin ( 4 4 ^{\circ} )}