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

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

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sin(67.5)cos(22.5)

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

\frac{2 + 2}{4}

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Use the following trivial identity:

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

= \frac{1 + \frac{2}{2}}{2}

Simplify

\frac{1 + \frac{2}{2}}{2} : \frac{2 + 2}{4}

= \frac{2 + 2}{4}

- π cos (π) + sin (π)

25 sin (6 0^{\circ})

cos (arccos (- 2))

800 cos (3 0^{\circ})

sec (2 5^{\circ})

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