What is the value of 8cos(22.5)*cos(67.5) ?

The value of 8cos(22.5)*cos(67.5) is 2sqrt(2)

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8cos(22.5)*cos(67.5)

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

22

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

= 4 (0 + \frac{2}{2})

Simplify

4 (0 + \frac{2}{2}) : 22

= 22

\frac{8}{tan ( 6 0 ^{\circ} )}

cot (arctan (\frac{3}{4}))

3 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

sin (arccos (- \frac{3}{4}))

3 tan (2 0^{\circ})

What is the value of 8cos(22.5)*cos(67.5) ?
The value of 8cos(22.5)*cos(67.5) is 2sqrt(2)