Question

Find the exact value using the sum/difference formula.

sin 140 degrees cos 50 degrees-cos 140 degrees sin 50 degrees

Answer 1

To find the exact value of sin 140° cos 50° - cos 140° sin 50°, we can use the sum/difference formula for sine and cosine:

sin (a - b) = sin a cos b - cos a sin b

cos (a - b) = cos a cos b + sin a sin b

Using these formulas, we can write:

sin 140° cos 50° - cos 140° sin 50°

= sin (140° - 50°)

= sin 90°

= 1

Therefore, the exact value of sin 140° cos 50° - cos 140° sin 50° is 1.