Question

Find the exact value of each of the following under the given conditions below. 3x sin a= 3 50 2 <«< -*; tan B = - 13. 3 <B<x (a) sin(a+B) (b) cos (a + b) (c) sin(a-B) (d) tan (a - B) (a) sin(a+B)= 1 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (b) cos (a + b) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (c) sin (a - b) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (d) tan (a - b) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer 1

given sina = 3/5 - 31 <4 L-X we know that sina & cosx = 1 >> cosaa -sina cosa = 1 / - (31" 7 Cosa = I V L-2 IC » Cosa - cosa = I 4/5 In -3*<L-* cosa = 24/5 .. Given tan B = -√3 7/2 <BLR we know that sec plans = - Secß = 1 Vitrans = 7+(-V3) - = V1+3 = 12 In 7/2 <BLA, Secß = -2 2 1 cos cosis > Cosp =-12 and $150 sin B + costs = 1 » SinB = 1 Vi-Cosis = + VI-6-1ja = 1 V 4- 42 - 4 in / LB La 2 sinB = + 3/2

ca) sin(x +B) = sina cosB + cost sinß = 3/5 *(-) + (-4/5) * 483 El ( 31403 10 3 10 1 10 (b) cos(x+1) = cosa COSB - Sina sing x(-12) (3/5-) * -4/5 r3 383 70 4-373 10 ܘܐ c) sin(x-B) = sina cosB - cosa sinB 315 *(-12) (-4/5) 3 = + To 463 10 - 3+ 473 10 ad fan (x-3) = lana - tanx fan B It hana tanp sina a N cosas tana = 3/5 2315 -415 -415 = -3/4 - (-13) 17 (-34) (-13) -3/4] 11 - 344+03 그 - 3+413 4+3/3 It 3v3