What is the value of sin(75)sin(15) ?

The value of sin(75)sin(15) is 1/4

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sin(75)sin(15)

sin (7 5^{\circ}) sin (1 5^{\circ})

\frac{1}{4}

Solution steps

sin (7 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 6 0 ^{\circ} ) - cos ( 9 0 ^{\circ} )}{2}

= \frac{cos ( 6 0 ^{\circ} ) - cos ( 9 0 ^{\circ} )}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

= \frac{\frac{1}{2} - 0}{2}

Simplify

\frac{\frac{1}{2} - 0}{2} : \frac{1}{4}

= \frac{1}{4}

\frac{tan ( 7 4 ^{\circ} ) - tan ( 1 4 ^{\circ} )}{1 + tan ( 7 4 ^{\circ} ) tan ( 1 4 ^{\circ} )}

7 sin (3 5^{\circ})

sin (\frac{π}{20})

cos (\frac{π}{3} - \frac{π}{4})

cos (arctan (\frac{24}{7}))