Question

Find the exact value of sin​(​α-β) if sin(α)=8/17 and sin(β)=5/13 and α and β are between 0 and ​π/2.

Answer 1

Explanation:

Since alpha a beta are in the first quadrant, the values of cos and sin for them are positive.

Trig identities

sinΦ ^2 + cos Φ^2 = 1

Using this identity, then cos a = 15/17 cos b = 12/13

Next , sub in the values using this trig identity:

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

= (8/17) (12/13) - (15/17)(5/13) = 21/221