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

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

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sec(pi/4)tan(pi/4)-sqrt(2)sec^2(pi/4)

sec (\frac{π}{4}) tan (\frac{π}{4}) - 2 sec^{2} (\frac{π}{4})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

sec (\frac{π}{4}) tan (\frac{π}{4}) - 2 sec^{2} (\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

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

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

Simplify

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

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

Multiply:

2 \cdot 1 = 2

= 2 - 2 (2)^{2}

(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 - 22

Add similar elements:

2 - 22 = - 2

= - 2

= - 2

\frac{5}{tan ( 4 0 ^{\circ} )}

cos (\frac{1 π}{3})

sec (arctan (- 8))

10 \cdot cos (3 5^{\circ})

sin (arctan (0))

What is the value of sec(pi/4)tan(pi/4)-sqrt(2)sec^2(pi/4) ?
The value of sec(pi/4)tan(pi/4)-sqrt(2)sec^2(pi/4) is -sqrt(2)