What is the value of sin(105)sin(75) ?

The value of sin(105)sin(75) is (sqrt(3)+2)/4

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sin(105)sin(75)

sin (10 5^{\circ}) sin (7 5^{\circ})

\frac{3 + 2}{4}

Solution steps

sin (10 5^{\circ}) sin (7 5^{\circ})

Rewrite using trig identities:

\frac{cos ( 3 0 ^{\circ} ) - cos ( 18 0 ^{\circ} )}{2}

= \frac{cos ( 3 0 ^{\circ} ) - cos ( 18 0 ^{\circ} )}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

= \frac{\frac{3}{2} - ( - 1 )}{2}

Simplify

\frac{\frac{3}{2} - ( - 1 )}{2} : \frac{3 + 2}{4}

= \frac{3 + 2}{4}

250 sec^{2} (\frac{π}{3})

arccos (0.342)

tan (\frac{8}{7})

arccos (\frac{19}{406})

cos (\frac{10}{8})

What is the value of sin(105)sin(75) ?
The value of sin(105)sin(75) is (sqrt(3)+2)/4