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

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

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sin(37.5)cos(7.5)

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

\frac{2 + 1}{4}

Solution steps

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

arccsc (8)

arccsc (6)

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

\frac{sin ( 0.5 )}{0.5}

1 - sin (3 5^{\circ})

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