Question

Sin407×cos87-cos407×sin87

Answer 1

$sin407\cdot cos87-cos407\cdot sin87=sin(407-87)=sin320=\\\\=sin(360-40)=sin(-40)=-sin40$

Answer 2

To evaluate the expression sin(407) × cos(87) - cos(407) × sin(87), you need to use trigonometric identities and convert the angles to radians.

First, convert the angles from degrees to radians by multiplying them by π/180:

407 degrees = 407 × π/180 radians 87 degrees = 87 × π/180 radians

Now you can rewrite the expression:

sin(407) × cos(87) - cos(407) × sin(87) = sin(407 × π/180) × cos(87 × π/180) - cos(407 × π/180) × sin(87 × π/180)

Using the trigonometric identities sin(a - b) = sin(a) × cos(b) - cos(a) × sin(b) and cos(a - b) = cos(a) × cos(b) + sin(a) × sin(b), you can simplify the expression further:

= sin(407 × π/180 - 87 × π/180)

Now, evaluate the angle in radians:

= sin((407 - 87) × π/180) = sin(320 × π/180)

Finally, calculate the value:

= sin(320π/180) = sin(16π/9)

At this point, the value of sin(16π/9) cannot be simplified further unless you have specific instructions or a table of values to work with.