What is the value of cos(37.5)sin(7.5) ?

The value of cos(37.5)sin(7.5) is (sqrt(2)-1)/4

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cos(37.5)sin(7.5)

cos (37. 5^{\circ}) sin (7. 5^{\circ})

\frac{2 - 1}{4}

Solution steps

cos (37. 5^{\circ}) sin (7. 5^{\circ})

Rewrite using trig identities:

\frac{sin ( 4 5 ^{\circ} ) - sin ( 3 0 ^{\circ} )}{2}

= \frac{sin ( 4 5 ^{\circ} ) - sin ( 3 0 ^{\circ} )}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{\frac{2}{2} - \frac{1}{2}}{2}

Simplify

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

= \frac{2 - 1}{4}

sin (6 6^{\circ})

1 - cos (2 π)

2 tan (\frac{π}{4})

sec (- 2 π)

7 cos (3 0^{\circ})

What is the value of cos(37.5)sin(7.5) ?
The value of cos(37.5)sin(7.5) is (sqrt(2)-1)/4