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: tan alpha= - 8/15, alpha lies in quadrant II, and cos beta= 3/4, beta lies in quadrant I a. sin (alpha + beta) b. cos (alpha + beta) c. tan (alpha + beta)

Solution

a). sin(+b) = sincosb +cos.sinb

we know that tan = -8/15

sec^2 -tan^2 =1

sec^2 = 1 +64/225

sec^2 = 289/225

sec = -17/15 [ is in QII]

now cos = -15/17

and sin = 8/17

cos =3/4

then sin = sqrt(7)/4

sin(+) = sincos +cos.sin

= 8/17 . 3/4 + -15/17 . sqrt(7)/4

= 24/68 - 15sqrt(7)/68

= [ 24 - 15.sqrt(7) ]/68

b).cos(+) = coscos -sin.sin

= -15/17 .3/4 - 8/17.sqrt(7)/4

= - [ 45+8sqrt(7)]/68

c).tan(a+b) = sin(a+b) /cos(a+b)

= [ 24 - 15.sqrt(7) ] / - [ 45+8sqrt(7)]