What is the value of 7sec(pi/4)+5cot(pi/4) ?

The value of 7sec(pi/4)+5cot(pi/4) is 7sqrt(2)+5

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7sec(pi/4)+5cot(pi/4)

7 sec (\frac{π}{4}) + 5 cot (\frac{π}{4})

72 + 5

Decimal Notation

14.89949 \dots

Solution steps

7 sec (\frac{π}{4}) + 5 cot (\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:

cot (\frac{π}{4}) = 1

cot (\frac{π}{4})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= 72 + 5 \cdot 1

Simplify

= 72 + 5

cos (arccos (2.1))

cos (π (0))

- 3 cos (- \frac{7 π}{6})

- cos (\frac{2 π}{2})

\frac{20}{sin ( 3 5 ^{\circ} )}

What is the value of 7sec(pi/4)+5cot(pi/4) ?
The value of 7sec(pi/4)+5cot(pi/4) is 7sqrt(2)+5