Find the exact value of each of the following under the give

Find the exact value of each of the following under the given conditions, cos (alpha + beta) sin (alpha + beta) tan (alpha + beta) tan alpha = 2/3, pi

Solution

Tan = 2/3        (III quadrant)

Sec = -13/3

Cos = -3/13

Sin = -2/13

Cos = ½         (IV quadrant)

Sin = -3/2

Tan = -3

a) cos( + ) = cos*cos – sin*sin = (-3/13)*(1/2) – (-2/13)*( -3/2) = -(1/13)*(1.5 + 3)

b) sin( + ) = sin cos + cos sin = (-2/13)*(1/2) + (-3/13)*( -3/2) = -(1/13)*(1 - 33/2)

c) tan( + ) = sin( + )/cos( + ) = (1 - 33/2)/ (1.5 + 3)