Sin(150)cos(300)
=sin(180-150)cos(360-300)
=sin(30)cos(60)
=0.5×0.5
=0.25

To solve this problem, we need to know the values of sin and cos of 150 and 300 degrees.



To find sin 150 degrees, we can use the formula:

sin (180 - θ) = sin θ

Therefore, sin 150 degrees will be equal to sin (180 - 30) degrees which is the same as sin 30 degrees.

We know that sin 30 degrees is equal to 1/2, so sin 150 degrees = 1/2.



To find cos 300 degrees, we can use the formula:

cos (360 - θ) = cos θ

Therefore, cos 300 degrees will be equal to cos (360 - 60) degrees which is the same as cos 60 degrees.

We know that cos 60 degrees is equal to 1/2, so cos 300 degrees = 1/2.



Now that we have the values of sin 150 degrees and cos 300 degrees, we can multiply them together to get the final answer:

sin 150 degrees cos 300 degrees = (1/2) x (1/2) = 1/4.

Therefore, the value of sin 150 degrees cos 300 degrees is 1/4.