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

The value of 4sec^2(pi/4)tan^2(pi/4)+2sec^4(pi/4) is 16

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4sec^2(pi/4)tan^2(pi/4)+2sec^4(pi/4)

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

16

Solution steps

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

= 4 (2)^{2} \cdot 1^{2} + 2 (2)^{4}

Simplify

4 (2)^{2} \cdot 1^{2} + 2 (2)^{4} : 16

4 (2)^{2} \cdot 1^{2} + 2 (2)^{4}

Apply rule

1^{a} = 1

1^{2} = 1

= 4 \cdot 1 \cdot (2)^{2} + 2 (2)^{4}

4 (2)^{2} \cdot 1 = 8

4 (2)^{2} \cdot 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

= 4 \cdot 2 \cdot 1

Multiply the numbers:

4 \cdot 2 \cdot 1 = 8

= 8

2 (2)^{4} = 2^{3}

2 (2)^{4}

(2)^{4} = 2^{2}

(2)^{4}

Apply radical rule:

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

= (2^{\frac{1}{2}})^{4}

Apply exponent rule:

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

= 2^{\frac{1}{2} \cdot 4}

\frac{1}{2} \cdot 4 = 2

\frac{1}{2} \cdot 4

Multiply fractions:

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

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= 2^{2}

= 2^{2} \cdot 2

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

= 2^{1 + 2}

Add the numbers:

1 + 2 = 3

= 2^{3}

= 8 + 2^{3}

2^{3} = 8

= 8 + 8

Add the numbers:

8 + 8 = 16

= 16

= 16

cos (π - 1) \cdot 0.2

\frac{cos ( 0.002 ) - 1}{0.00 2 ^{2}}

\frac{cos ( 2 ( 0.001 ) ) - cos ( 0.001 )}{0.00 1 ^{2}}

cot (arcsin (\frac{12}{13}))

2 cos (6)

What is the value of 4sec^2(pi/4)tan^2(pi/4)+2sec^4(pi/4) ?
The value of 4sec^2(pi/4)tan^2(pi/4)+2sec^4(pi/4) is 16