What is the value of sin(85)cos(25)-sin(25)cos(85) ?

The value of sin(85)cos(25)-sin(25)cos(85) is (sqrt(3))/2

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sin(85)cos(25)-sin(25)cos(85)

sin (8 5^{\circ}) cos (2 5^{\circ}) - sin (2 5^{\circ}) cos (8 5^{\circ})

\frac{3}{2}

Solution steps

sin (8 5^{\circ}) cos (2 5^{\circ}) - sin (2 5^{\circ}) cos (8 5^{\circ})

Rewrite as

= sin (8 5^{\circ}) cos (2 5^{\circ}) - cos (8 5^{\circ}) sin (2 5^{\circ})

Rewrite using trig identities:

sin (6 0^{\circ})

= sin (6 0^{\circ})

Use the following trivial identity:

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

= \frac{3}{2}

1 + 2 cos (π)

cos (2 \cdot \frac{3 π}{2})

9 sin (3 0^{\circ})

cos (- \frac{2}{5})

cos (\frac{\frac{4 π}{3}}{2})

What is the value of sin(85)cos(25)-sin(25)cos(85) ?
The value of sin(85)cos(25)-sin(25)cos(85) is (sqrt(3))/2