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

The value of sec(pi/3)-sec(pi/4) is 2-sqrt(2)

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

sec (\frac{π}{3}) - sec (\frac{π}{4})

2 - 2

Decimal Notation

0.58578 \dots

Solution steps

sec (\frac{π}{3}) - sec (\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:

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

= 2 - 2

sin (\frac{7}{9})

cos (7 π) + sin (7 \frac{π}{2})

arctan (\frac{40}{60})

sin^{2} (6 0^{\circ}) + cos^{2} (3 0^{\circ})

150 cos (2 0^{\circ})

What is the value of sec(pi/3)-sec(pi/4) ?
The value of sec(pi/3)-sec(pi/4) is 2-sqrt(2)