What is the value of 2sin(157.5)cos(157.5) ?

The value of 2sin(157.5)cos(157.5) is -(sqrt(2))/2

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2sin(157.5)cos(157.5)

2 sin (157. 5^{\circ}) cos (157. 5^{\circ})

- \frac{2}{2}

Solution steps

2 sin (157. 5^{\circ}) cos (157. 5^{\circ})

Rewrite using trig identities:

sin (31 5^{\circ})

= sin (31 5^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (13 5^{\circ}) + cos (18 0^{\circ}) sin (13 5^{\circ})

= sin (18 0^{\circ}) cos (13 5^{\circ}) + cos (18 0^{\circ}) sin (13 5^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

sec (3 5^{\circ})

2 \cdot sin (\frac{π}{4})

tan (arcsec (4))

sin (13 π)

arctan (\frac{3}{9})

What is the value of 2sin(157.5)cos(157.5) ?
The value of 2sin(157.5)cos(157.5) is -(sqrt(2))/2