Question

Find the exact value of the expressions

cos(α+β)​,

sin(α+β)

and

tan(α+β)

under the following​ conditions:

sin(α)=4/5​,α lies in quadrant​ I, and sin(β)=15/17​,β lies in quadrant II.

Answer 1

The solutions are given below

Given that sing=4 un 32 And we know that (632= I-S1624 So, Cosy z1-14 12 16 5 25 25-16 23 25 Cosa 5 And tana sina 47 u Cosa 3 3/6 tanazy And 225 289 17 that given Sinß- 15 17 So, 6832 = 1-1512 117 299 209-225 64 209 les ß = 1 is in Ind quadrant, so it is Cosß . 15114 - 15 1838 But B negative, so 8 Thus, tauß = sink -B/17 Famß -15 8

Now cos&+B) = (a los p -sin sinß 517 -24-60 17X5 05 Cook +B) - - 84 3 (ott y 15 -24 Go 05 05 13 85 And Sin K+B) = sing bis B t losa sin ß 4 -9 + 3 15 5 17) 17 -32 45 -32745 + 85 05 Sink+)=13 05 And tan R+B). tamkt tan ß - tana tanß + (-15/0) - 4 =15 24 / 15 3245 24 1+ 60 2 24 too 24 tanlatß) - 13 Ay