What is the value of 2sin(112.5)cos(112.5) ?

The value of 2sin(112.5)cos(112.5) is -(sqrt(2))/2

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2sin(112.5)cos(112.5)

2 sin (112. 5^{\circ}) cos (112. 5^{\circ})

- \frac{2}{2}

Solution steps

2 sin (112. 5^{\circ}) cos (112. 5^{\circ})

Rewrite using trig identities:

sin (22 5^{\circ})

= sin (22 5^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (4 5^{\circ}) + cos (18 0^{\circ}) sin (4 5^{\circ})

= sin (18 0^{\circ}) cos (4 5^{\circ}) + cos (18 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

tan (\frac{7 π}{6} + \frac{π}{4})

arcsin (\frac{6.1}{9.9})

25 cos (7 5^{\circ})

cos (arcsin (\frac{3}{5}) - arccos (\frac{1}{2}))

sec (\frac{11 π}{2})

What is the value of 2sin(112.5)cos(112.5) ?
The value of 2sin(112.5)cos(112.5) is -(sqrt(2))/2