What is the value of sec(-pi/3)-cot(-(5pi)/4) ?

The value of sec(-pi/3)-cot(-(5pi)/4) is 3

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sec(-pi/3)-cot(-(5pi)/4)

sec (- \frac{π}{3}) - cot (- \frac{5 π}{4})

3

Solution steps

sec (- \frac{π}{3}) - cot (- \frac{5 π}{4})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{5 π}{4}) = - cot (\frac{5 π}{4})

= sec (- \frac{π}{3}) - (- cot (\frac{5 π}{4}))

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{3}) = sec (\frac{π}{3})

= sec (\frac{π}{3}) - (- cot (\frac{5 π}{4}))

cot (\frac{5 π}{4}) = cot (\frac{π}{4})

cot (\frac{5 π}{4})

Rewrite

\frac{5 π}{4}

π + \frac{π}{4}

= cot (π + \frac{π}{4})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{π}{4}) = cot (\frac{π}{4})

= cot (\frac{π}{4})

= sec (\frac{π}{3}) - (- cot (\frac{π}{4}))

Simplify

= sec (\frac{π}{3}) + cot (\frac{π}{4})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

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

= 2 + 1

Simplify

= 3

49 cos (3 0^{\circ})

sec (- 5 π)

\frac{1}{sin ( 4 8 ^{\circ} )}

tan (28 0^{\circ})

\frac{5}{cos ( 5 0 ^{\circ} )}

What is the value of sec(-pi/3)-cot(-(5pi)/4) ?
The value of sec(-pi/3)-cot(-(5pi)/4) is 3