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

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

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

cos (\frac{4 π}{3} - \frac{3 π}{4})

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

Solution steps

cos (\frac{4 π}{3} - \frac{3 π}{4})

Simplify:

\frac{4 π}{3} - \frac{3 π}{4} = \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}

cos^{2} (\frac{7 π}{8})

3 + 2 sin (- \frac{π}{6})

\frac{60 sin ( 1 5 ^{\circ} )}{400}

- tan^{2} (0)

e^{2 s i n (\frac{π}{2})}

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