Question

question 47 and 48 please. Thanks

43. tan” x - 2 tan x = 0 44. 2 tan” x - 3 tan x = -1 45. tan- 0 + tan 0 - 6 = 0 46. sec? x + 6 tan x + 4 = 0 2.4 Evaluating Trigonometric Functions in Exercises 47-50, find the exact values of the sine, cosine and tangent of the angle. 47. 75º = 120° - 45° 48. 375º = 135° + 240° 402511 - 117 50. 191 - 111_1 12 6 4 12 6 4 Rewriting a Trigonometric Expression In Exercises 51 and 52, write the expression as the sine, cosine, or tangent of an angle. 51. sin 60° cos 45º – cos 60° sin 45° 52 tan 68° - tan 115° 1 + tan 68° tan 115° Evaluating a Trigonometric Expression Exercises 53–56, find the exact value of the trigono expression given that tan u = and cos y = -5. Quadrant I and v is in Quadrant III.) 53. sin(u + v) he trigonometric V= -. (u is in

Answer 1

According to the question we can directly use the general formula of trigonometry, here given 75=120-45 and 375=135+240.so we can use :

sin(A-B)=sinAcosB-cosAsinB

cos(A-B)=cosAcosB+sinAsinB

Hence for tangent of the angle we candirectly use the formula, tan(A-B)=sin(A-B)/cos(A-B).

similarly for the quetion no 48.

sin(A+B)=sinAcosB+cosAsinB

cos(A+B)=cosAcosB-sinAsinB

tan(A+B)=sin(A+B)/cos(A+B)

ans to Q.47:

47. Solutom Givem - 120 ° 45-0 75° Sim 75°= sim ( 120°-45) = Sim 120° Cos 4 5°- Cos 120°sim 45° I Sim (A-B) = SimA Cous B - CoSA SimBl = Sim (904 30°) Cosu50- Cob(90°t30°) Sim 450 = Curs 30° Cosus0_(-sim 30°) simu5° T: Sim (900+) =CosO onel Cus (90t ©) = - Simo] V2 VE 212 212 V3+1 [ Multiplyimg mumerator and demomimator by VR] V6+V2 : Sim 75° =

Cors 75° = = Cors (120°-45°) - Cob120" Ces 450. + sim 120° Sim45-0 [ Cos (A-B) = CobA Cens B + SiMA SimB] = Cuis (90°t 30°) Cois450+ Sim (900+ 30°) Simu50 - Sim 30° asu5° + Con 30' sim450 [ Cos(90°40)=-Simo [: Cos (90°to)=-Simo and sim(90°t co) = Cers@] V2 쭈+ 무사두 2V2 212 VB -1 VE- VZ [ Multiplying mumeratoy and denomimator by 2I V6- V2 '. Cos 75°=

and Ham 75° = tam (120°-450) Sim A sim (120°-45 ) [: tam A = Cors A Cors (120°-45°) VE +V2 V6 - V2 VE+V2 -Z2 N6 -V2 (VEt VZ) (VZ +VZ) (VE-VZ) (VE+VZ) (VE)+ (Vã )² + 2 VEVZ NE )2-CVE)2 6+2+2 Vi2 : (a-b) catb) = a? -6? Catb)?= a?t b2+2ab 6-2 2+2 V4x3 8 +4 3 %3D 4(2+3) 2 2+ V3 tam a56 2+V3
.

ans to Q.48:

48. Solutiom Givem. 375 = 135 + 240" = Sim (135 + 240°) : Sim (375") : Sim 2406 sim 135 Cos 240°+ Cos 135° Sim (90'+45°) Cos (180t60°) %3D + Cors (90st 45°)Sim(1304 60") = Cos45° (-CosG0) + (-sim 45°) (-sinGo") - Cos45° Cus60°+Sin45°sim 60" %3D V2 V3 IN 2V2 2VZ N3-1 VZ (V3 -1) (By omultiplynng denoonimator by VZ) bosh numerator amd V2 (2vZ) N6 -N2 Sim (375") =

Cets (875) = Ces (135°+ 240°) Sim135°Sim 240° = Cus135° Cus240°- Cas (90°+45°) cors (130°t 60°) - Sim(9u°t45") sim(180°t 60°) = -simus E cos 60°) - Cus45° (- simGo°) Sim45° CursG0°+ Cos456 simGo %3D V2 2V2 212 V3+) 2V2 VZ(V341) VI(2N2) (By multiplying bosh mumerator and demomimator by VZ) .. Cos 3750 =

amd tan375°= tan (13 5-°+ 240°) Sim CA+A) Sin (1350+ 240°) [: Ham CATB) = Cus CA+B Cos (1350+240") NE - VZ 4 NT-V2 VG- VZ (V2 -Vz) (VE-Vz) [: (utb) (a-b) za2ab2 (a-b)2= a2+ b2-2ub (V8 +VZ) (VE-Vz) (ve )2 + (vz)2vē vZ 6+ 2-2VIE 6 -2 8 - 3 V413 2 -413 :-bn 3752 2 - 13