 | Olinthus Gregory - 1816 - 278 Seiten
...taking away the denominator, tan c — tan A tan B tan c = — tan A — tan B, and, by transposition, tan A + tan B + tan c = tan A tan B tan c. . , . {4.) Dividing this equation by the whole of the first member, and substituting for the products of the tangents... | |
 | Daniel Cresswell - 1816 - 352 Seiten
...KB. 22", « (28).. .sin (^1 + J3) + sin (A + 2B) + &c. + sin(.4 +nB) = 0. If ^ + B + C=180°, (30). . .tan A + tan B + tan C = tan A tan B tan C. (31).. .tan (A + B) + tzn C = 0. If A + B + C= ( 2« + 1) 90°, *(32)...cot A + cot B + cot C=cot A... | |
 | John Radford Young - 1833 - 286 Seiten
...arcs . ib. 27. Proof that the angles A, B, C, of a plane triangle have this remarkable property, viz. tan. A + tan. B + tan. C = tan. A tan. B tan. C . 49 28. Formulas for multiple arcs . . . ib. 29. Investigation of De Moivre's Formula . . .51 30.... | |
 | Augustus De Morgan - 1837 - 258 Seiten
...sin C cos A Again, tan (A + B) = — tan C = - -: - ^ , . . -,. _ Ian A + tan B ^ ' 1— tanA.tanB or tan A + tan B + tan C = tan A . tan B . tan C (82.) Let pV, q\J, and rU, be the three perpendiculars let fall from the vertices of the triangle upon... | |
 | Alfred Wrigley - 1845 - 222 Seiten
...tan C. 79. cot A . cot B + cot A . cot C + cot B . cot С = 1 . 80. If A + B + C = 45°, prove that tan A + tan B + tan C —tan A . tan B . tan C = 1 —tan A . tan B . —tan A . tan C — tan . tan C. If A, B and C be in arithmetical progression,... | |
 | John Radford Young - 1855 - 218 Seiten
...the supplement of A + B, tan (A + B) = — tan C, hence (II) _ tan .4+ tan .B 1 — tan.4 la,nB .'. tan A tan B tan C= tan A + tan B + tan C that is, the product of the tangents of the angles is equal to the swm. If the three angles, instead... | |
 | Alfred Wrigley - 1857 - 332 Seiten
...+ C = 90° ; prove that— 1. tanAtanB + tan AtanC+tanBtanC=1. 2. cotA + cotB + cotC=cotAcotBcotC. 3. tan A + tan B + tan C = tan A tan B tan C + sec A sec B sec C. 4. sin 2A + sin 2B + sin 2C =4 cos A cos B cos C. cos A + sin C — sin B 1 +... | |
 | War office - 1858 - 578 Seiten
...triangle, of which A, B, C, are the angles, and (a), (6), (c), the sides subtending them, prove — (1.) Tan A + tan B + tan C = tan A. tan B .tan C. ._. AB 0-6 C (2.) Sm -g— = — - — cos g' 3. From the edge of one bank of a river a person ascends... | |
 | Isaac Todhunter - 1860 - 318 Seiten
...-= + (y — ») cot -^ + (z — x) cot -= = 0. 55. If A + B + C = mir where m is any integer, then tan A + tan B + tan C = tan A tan B tan C. 56. If a, 8, y be any angles, shew that nia PV sin a + sin p + sm y — 4 cos ^ cos ^ cos — ,., .... | |
 | Alfred Wrigley - 1862 - 330 Seiten
...sin -- f- sin ( A + B + C) . 222 41. cosA + cosB+cosC=4cos - cos -- cos ----- cos(A + B + C). 222 42. tan A + tan B + tan C = tan A tan B tan C + 43. sin A sm 15 sin L 44. 4sini(A + B + C)sini(B + C - A)sini(A + C -B)sini(A + B - C) = i — cos1... | |
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C = 1 + 4 sin £A sin £B sin £C. 37. tan A + tan B + tan C = tan A tan B tan C. 
