What is the value of cos(52.5)sin(7.5) ?

The value of cos(52.5)sin(7.5) is (sqrt(3)-sqrt(2))/4

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cos(52.5)sin(7.5)

cos (52. 5^{\circ}) sin (7. 5^{\circ})

\frac{3 - 2}{4}

Solution steps

cos (52. 5^{\circ}) sin (7. 5^{\circ})

Rewrite using trig identities:

\frac{sin ( 6 0 ^{\circ} ) - sin ( 4 5 ^{\circ} )}{2}

= \frac{sin ( 6 0 ^{\circ} ) - sin ( 4 5 ^{\circ} )}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

= \frac{\frac{3}{2} - \frac{2}{2}}{2}

Simplify

\frac{\frac{3}{2} - \frac{2}{2}}{2} : \frac{3 - 2}{4}

= \frac{3 - 2}{4}

cot^{2} (3 0^{\circ})

arctan (\frac{- 1}{0})

\frac{100}{sin ( 3 0 ^{\circ} )}

\frac{5}{cos ( 4 5 ^{\circ} )}

csc (arccos (\frac{7}{25}))

What is the value of cos(52.5)sin(7.5) ?
The value of cos(52.5)sin(7.5) is (sqrt(3)-sqrt(2))/4