Evaluate sin (π/4) cos (π/6) - sin (π/6) cos (π/4)?

Solution:

Given sin (π/4) cos (π/6) - sin (π/6) cos (π/4)

This is in the form sinAcosB - cosAsinB

Here, A = π/4 and B = π/6

We know that sinAcosB - cosAsinB = sin(A - B)

Hence, sin(π/4 - π/6 ) = sin(45° - 30°) = sin15°

Sin15° = 0.25

Therefore, sin (π/4) cos (π/6) - sin (π/6) cos (π/4) = 0.25

Evaluate sin (π/4) cos (π/6) - sin (π/6) cos (π/4)?

Summary:

By evaluating, we get sin (π/4) cos (π/6) - sin (π/6) cos (π/4) = 0.25