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

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

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sin(67.5)sin(22.5)

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

\frac{2}{4}

Solution steps

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

- 7 sin (\frac{π}{2})

csc (- 51 0^{\circ})

sin (arcsin (1) + arccos (1))

40 \cdot \frac{sin ( 13 5 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

8 sin (29 0^{\circ}) + 6 sin (6 0^{\circ})

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