What is the value of cos((7pi)/(24))sin(pi/(24)) ?

The value of cos((7pi)/(24))sin(pi/(24)) is (sqrt(3)-sqrt(2))/4

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cos((7pi)/(24))sin(pi/(24))

cos (\frac{7 π}{24}) sin (\frac{π}{24})

\frac{3 - 2}{4}

Solution steps

cos (\frac{7 π}{24}) sin (\frac{π}{24})

Rewrite using trig identities:

\frac{sin ( \frac{π}{3} ) - sin ( \frac{π}{4} )}{2}

= \frac{sin ( \frac{π}{3} ) - sin ( \frac{π}{4} )}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \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}

e^{c o s (\frac{π}{2})}

tan (94 5^{\circ})

sin (3 \cdot \frac{π}{4})

sec^{2} (1 0^{\circ})

sec (1 7^{\circ})

What is the value of cos((7pi)/(24))sin(pi/(24)) ?
The value of cos((7pi)/(24))sin(pi/(24)) is (sqrt(3)-sqrt(2))/4