What is the value of cos((2pi)/3-(5pi)/4) ?

The value of cos((2pi)/3-(5pi)/4) is (sqrt(2)(1-sqrt(3)))/4

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cos((2pi)/3-(5pi)/4)

cos (\frac{2 π}{3} - \frac{5 π}{4})

\frac{2 ( 1 - 3 )}{4}

Solution steps

cos (\frac{2 π}{3} - \frac{5 π}{4})

Simplify:

\frac{2 π}{3} - \frac{5 π}{4} = - \frac{7 π}{12}

= cos (- \frac{7 π}{12})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{7 π}{12}) = cos (\frac{7 π}{12})

= cos (\frac{7 π}{12})

Rewrite using trig identities:

cos (\frac{π}{3}) cos (\frac{π}{4}) - sin (\frac{π}{3}) sin (\frac{π}{4})

= cos (\frac{π}{3}) cos (\frac{π}{4}) - sin (\frac{π}{3}) sin (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= \frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

Simplify

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( 1 - 3 )}{4}

= \frac{2 ( 1 - 3 )}{4}

arctan (\frac{\frac{1}{2}}{\frac{1}{2}})

sin (26 0^{\circ}) cos (2 0^{\circ}) - cos (26 0^{\circ}) sin (2 0^{\circ})

- ln (cos (1))

arcsin (- \frac{2}{3})

arcsec (\frac{6}{5})

What is the value of cos((2pi)/3-(5pi)/4) ?
The value of cos((2pi)/3-(5pi)/4) is (sqrt(2)(1-sqrt(3)))/4