Trig Identities Quiz

Which of the following is a Pythagorean trigonometric identity?

• Both A and B

Answer explanation

Using the sum identity for sine, sin(5π/12) = sin(π/4 + π/3) = sin(π/4)cos(π/3) + cos(π/4)sin(π/3) = (√2/2 * √3/2) + (√2/2 * 1/2) = (√6 + √2)/4

Answer explanation

Using the sum identity for cosine, we have cos(7π/12) = cos(π/3 + π/4) = cos(π/3)cos(π/4) - sin(π/3)sin(π/4) = (sqrt(3)/2 * sqrt(2)/2) - (sqrt(3)/2 * sqrt(2)/2) = -sqrt(6)/4 + sqrt(2)/4 = -sqrt(6 - sqrt(2))/4