Suppose alpha and beta are acute angles such that cosalpha

Suppose alpha and beta are acute angles such that cos(alpha) = 3/5 and cos(beta) = 7/25. What is cos (alpha + beta)? Suppose alpha is an angle in quadrant II such that sin(alpha) = 3/5 and beta is an angle in quadrant III such that sec(beta) = -13/12. What is tan (alpha - beta)?

Solution

1) cosalpha = 3/5 ; sinalpha = 4/5

cosbeta = 7/25 ;sin beta = 24/25

Use identity : cos( alpha + beta) = cosalphacosbeta - sinalphasinbeta

= (3/5)(7/25) - (4/5)(24/25)

= -75/125 = - 3/5