What is the value of 4(sin(150))(cos(210))+3(tan(240)) ?

The value of 4(sin(150))(cos(210))+3(tan(240)) is 2sqrt(3)

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4(sin(150))(cos(210))+3(tan(240))

4 (sin (15 0^{\circ})) (cos (21 0^{\circ})) + 3 (tan (24 0^{\circ}))

23

Solution steps

4 (sin (15 0^{\circ})) (cos (21 0^{\circ})) + 3 (tan (24 0^{\circ}))

= 4 sin (15 0^{\circ}) cos (21 0^{\circ}) + 3 tan (24 0^{\circ})

Rewrite using trig identities:

4 sin (15 0^{\circ}) cos (21 0^{\circ}) = 2 (sin (0) - sin (6 0^{\circ}))

= 2 (sin (0) - sin (6 0^{\circ})) + 3 tan (24 0^{\circ})

tan (24 0^{\circ}) = tan (6 0^{\circ})

= 2 (sin (0) - sin (6 0^{\circ})) + 3 tan (6 0^{\circ})

Use the following trivial identity:

sin (0) = 0

Use the following trivial identity:

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

Use the following trivial identity:

tan (6 0^{\circ}) = 3

= 2 (0 - \frac{3}{2}) + 33

Simplify

2 (0 - \frac{3}{2}) + 33 : 23

= 23

30 sin (1 0^{\circ})

cos (3 (\frac{2 π}{3}))

cos (2 5^{\circ}) cos (2 0^{\circ}) - sin (2 5^{\circ}) sin (2 0^{\circ})

[2 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))]^{4}

\frac{5}{sin ( 4 0 ^{\circ} )}

What is the value of 4(sin(150))(cos(210))+3(tan(240)) ?
The value of 4(sin(150))(cos(210))+3(tan(240)) is 2sqrt(3)