What is the value of 3sec(pi/4)tan(pi/4)+10csc^2(pi/4) ?

The value of 3sec(pi/4)tan(pi/4)+10csc^2(pi/4) is 3sqrt(2)+20

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3sec(pi/4)tan(pi/4)+10csc^2(pi/4)

3 sec (\frac{π}{4}) tan (\frac{π}{4}) + 10 csc^{2} (\frac{π}{4})

32 + 20

Decimal Notation

24.24264 \dots

Solution steps

3 sec (\frac{π}{4}) tan (\frac{π}{4}) + 10 csc^{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

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= 32 \cdot 1 + 10 (2)^{2}

Simplify

32 \cdot 1 + 10 (2)^{2} : 32 + 20

32 \cdot 1 + 10 (2)^{2}

32 \cdot 1 = 32

32 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= 32

10 (2)^{2} = 20

10 (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

= 10 \cdot 2

Multiply the numbers:

10 \cdot 2 = 20

= 20

= 32 + 20

= 32 + 20

arccos (\frac{0}{2})

9 sin (\frac{π}{3})

sin (5 0^{\circ}) cos (4 0^{\circ}) + cos (5 0^{\circ}) sin (4 0^{\circ})

15 \cdot sin (4 0^{\circ})

5 sec^{2} (\frac{π}{4})

What is the value of 3sec(pi/4)tan(pi/4)+10csc^2(pi/4) ?
The value of 3sec(pi/4)tan(pi/4)+10csc^2(pi/4) is 3sqrt(2)+20