What is the value of 2sin(15)cos(75) ?

The value of 2sin(15)cos(75) is 1-(sqrt(3))/2

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2sin(15)cos(75)

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

1 - \frac{3}{2}

Solution steps

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

Rewrite using trig identities:

sin (9 0^{\circ}) - sin (6 0^{\circ})

= sin (9 0^{\circ}) - sin (6 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Use the following trivial identity:

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

= 1 - \frac{3}{2}

cot (arcsin (\frac{5}{13}))

arctan (- \frac{2}{2 3})

cos (\frac{5 π}{4} - \frac{7 π}{6})

- cos (2) (\frac{π}{2})

arcsin (\frac{5}{12 sin ( 3 5 ^{\circ} )})

What is the value of 2sin(15)cos(75) ?
The value of 2sin(15)cos(75) is 1-(sqrt(3))/2