What is the value of sin(105)sin(15) ?

The value of sin(105)sin(15) is 1/4

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sin(105)sin(15)

sin (10 5^{\circ}) sin (1 5^{\circ})

\frac{1}{4}

Solution steps

sin (10 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 9 0 ^{\circ} ) - cos ( 12 0 ^{\circ} )}{2}

= \frac{cos ( 9 0 ^{\circ} ) - cos ( 12 0 ^{\circ} )}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

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

Simplify

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

= \frac{1}{4}

sec^{2} (- π)

cos (180 0^{\circ})

2 csc^{2} (\frac{π}{3}) cot (\frac{π}{3})

30 sin (4 0^{\circ})

sec (\frac{5}{4})