What is the value of cos(67.5)cos(22.5) ?

The value of cos(67.5)cos(22.5) is (sqrt(2))/4

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cos(67.5)cos(22.5)

cos (67. 5^{\circ}) cos (22. 5^{\circ})

\frac{2}{4}

Solution steps

cos (67. 5^{\circ}) cos (22. 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 4 5 ^{\circ} ) + cos ( 9 0 ^{\circ} )}{2}

= \frac{cos ( 4 5 ^{\circ} ) + cos ( 9 0 ^{\circ} )}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

= \frac{\frac{2}{2} + 0}{2}

Simplify

\frac{\frac{2}{2} + 0}{2} : \frac{2}{4}

= \frac{2}{4}

62 cos (\frac{7 π}{4})

cot (arccsc (10))

arcsin (- 0.71)

2 cos^{2} (6 0^{\circ}) - 1

cos (- 90 0^{\circ})

What is the value of cos(67.5)cos(22.5) ?
The value of cos(67.5)cos(22.5) is (sqrt(2))/4