What is the value of cos((7pi)/4-(7pi)/6) ?

The value of cos((7pi)/4-(7pi)/6) is (sqrt(2)(1-sqrt(3)))/4

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cos((7pi)/4-(7pi)/6)

cos (\frac{7 π}{4} - \frac{7 π}{6})

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

Solution steps

cos (\frac{7 π}{4} - \frac{7 π}{6})

Simplify:

\frac{7 π}{4} - \frac{7 π}{6} = \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}

3 sec^{2} (\frac{π}{4})

cos (16 5^{\circ}) cos (4 5^{\circ}) + sin (16 5^{\circ}) sin (4 5^{\circ})

\frac{7}{tan ( 4 5 ^{\circ} )}

arcsin (1) - arcsin (- 1)

(sin (1))^{2}

What is the value of cos((7pi)/4-(7pi)/6) ?
The value of cos((7pi)/4-(7pi)/6) is (sqrt(2)(1-sqrt(3)))/4