What is the value of 4sin(187.5)cos(52.5) ?

The value of 4sin(187.5)cos(52.5) is -sqrt(3)+sqrt(2)

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4sin(187.5)cos(52.5)

4 sin (187. 5^{\circ}) cos (52. 5^{\circ})

- 3 + 2

Solution steps

4 sin (187. 5^{\circ}) cos (52. 5^{\circ})

Rewrite using trig identities:

2 (sin (24 0^{\circ}) + sin (13 5^{\circ}))

= 2 (sin (24 0^{\circ}) + sin (13 5^{\circ}))

Rewrite using trig identities:

sin (24 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

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

Simplify

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

= - 3 + 2

2 sin (- 1)

2 sin (- 2)

(sin^{2} (4 5^{\circ}) cos^{2} (4 5^{\circ}))^{\frac{3}{2}}

cot (\frac{- 11 π}{6})

arccos (\frac{3}{18})

What is the value of 4sin(187.5)cos(52.5) ?
The value of 4sin(187.5)cos(52.5) is -sqrt(3)+sqrt(2)