. A treatise on plane and spherical trigonometry. D A FUNDAMENTAL rOBMULA _1 Then tlic triangles BOB and BOA are mutually eqauUBgnlthe three sides of the one being perp. to the three sides of the Otherrespectively; therefore the angle B CE = A OB. Let x=AOB=BCE y = BOC Then, Fig. 10, x+y = COD Fig. 11, x-y=C0B and in Fls-10>8in (*+y) = (77)= co =co+~co „.««., v CD BA-CE BA CE , Bn(.-jr)-^-— ^ =-go--qq and in both figures #^L £A .5(9 . CO=^X(7(7 = sina;cos^02? Ctf C/? -co = c£xc7>=cos:csm^ which being substituted in the above expressions of sin [x + y) and sin (x — y) give sin (x -\
. A treatise on plane and spherical trigonometry. D A FUNDAMENTAL rOBMULA _1 Then tlic triangles BOB and BOA are mutually eqauUBgnlthe three sides of the one being perp. to the three sides of the Otherrespectively; therefore the angle B CE = A OB. Let x=AOB=BCE y = BOC Then, Fig. 10, x+y = COD Fig. 11, x-y=C0B and in Fls-10>8in (*+y) = (77)= co =co+~co „.««., v CD BA-CE BA CE , Bn(.-jr)-^-— ^ =-go--qq and in both figures #^L £A .5(9 . CO=^X(7(7 = sina;cos^02? Ctf C/? -co = c£xc7>=cos:csm^ which being substituted in the above expressions of sin [x + y) and sin (x — y) give sin (x -\- y) = sin a; cos y -f- cos x sin y (36) sin (x — y) — sin * cos y — cos x sin y (37) Again in „. „A , 6>2) OA-EB OA EB Fig. 10, ooi(« + jr)-^»—^y—-W-OT -,.„., , 02) OA + EB OA EB Fig. 11, cos (».- „) - OT - 0(7 = 0(7 + 0(7 and in both figures, 0A 0A 0B OC=OBXOC = cosxcosy EB EB BO . 0C==BCX0C = smxsu^ therefore cos {x + y) — cos x cos y — sin x sin y (38) cos (x — y) = cos z cos y -f sin x sin y (89) and
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Keywords: ., bookcentury1800, bookdecade1870, booksubjecttrigono, bookyear1876
