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

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

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cos(67.5)sin(22.5)

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

\frac{2 - 2}{4}

Solution steps

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

tan (- \frac{10 π}{3})

csc (39 0^{\circ})

cos (2 \cdot \frac{π}{3})

arccsc (- 3)

sin (\frac{π}{3}) + cos (\frac{π}{3})

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