Trigonometry ...1866 |
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Side 27
... tanB = 1 + tan A tanВ 31. The formulae in the four preceding Articles have only been proved for positive values of A , B , A + B and A - B , less than 90 ° . In the next Article , however , they will be shewn to hold universally for all ...
... tanB = 1 + tan A tanВ 31. The formulae in the four preceding Articles have only been proved for positive values of A , B , A + B and A - B , less than 90 ° . In the next Article , however , they will be shewn to hold universally for all ...
Side 31
... tanB Multiply the numerator and denominator of this fraction by cotД cotB , then since tan cotД = 1 , we have cotA cotB - 1 cot ( A + B ) : = cot.B + cotA In ( 1 ) and ( 2 ) put B = A . · ( 2 ) . 2tan A Then tan 2A = 1 - tan A ( 3 ) cot ...
... tanB Multiply the numerator and denominator of this fraction by cotД cotB , then since tan cotД = 1 , we have cotA cotB - 1 cot ( A + B ) : = cot.B + cotA In ( 1 ) and ( 2 ) put B = A . · ( 2 ) . 2tan A Then tan 2A = 1 - tan A ( 3 ) cot ...
Side 34
... tanB = -tan C ( 1- tanA tanB ) , .. tan4 + tanB + tanC = tan4 tanBtan C ...... ( 2 ) . 41. Let a + B + y = 2π , .. α = 2π- ( B + y ) , .. cosa = cos ( B + y ) = cosẞ cosy - sin ẞ siny , .. ( cosa - cosẞ cos y ) = sin2ß sin3y , .. cosa + ...
... tanB = -tan C ( 1- tanA tanB ) , .. tan4 + tanB + tanC = tan4 tanBtan C ...... ( 2 ) . 41. Let a + B + y = 2π , .. α = 2π- ( B + y ) , .. cosa = cos ( B + y ) = cosẞ cosy - sin ẞ siny , .. ( cosa - cosẞ cos y ) = sin2ß sin3y , .. cosa + ...
Side 45
... tanB = cot4 .. ab tanA = b cot B , b = atanB = a cot A. b = - a 52. In any triangle the sides are proportional to the sines of the opposite angles . ( 1 ) с A b A B α ( 2 ) A C D B α Let ABC be any triangle , and from A draw AD perpen ...
... tanB = cot4 .. ab tanA = b cot B , b = atanB = a cot A. b = - a 52. In any triangle the sides are proportional to the sines of the opposite angles . ( 1 ) с A b A B α ( 2 ) A C D B α Let ABC be any triangle , and from A draw AD perpen ...
Side 76
... tanB tan C. cosec 24 + cosec 2B + cosec 2 C = 0 , then will tan ( A — A ' ) = tan ( B — B ′ ) = tan ( C — C ' ) . - 14. Prove by a Geometrical construction , that tan ( A - B ) = tan Atan B 1 + tan A tan B and deduce the expansion of ...
... tanB tan C. cosec 24 + cosec 2B + cosec 2 C = 0 , then will tan ( A — A ' ) = tan ( B — B ′ ) = tan ( C — C ' ) . - 14. Prove by a Geometrical construction , that tan ( A - B ) = tan Atan B 1 + tan A tan B and deduce the expansion of ...
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angle POX increases angles terminated Cambridge centre circular measure coincides Conic Sections cos(a cos² cos4 cosB cosB+ cosec cosine cotA cotangent D.D. Dean D.D. Third Edition Dean of Ely decreases numerically Euclid EXAMPLES ON CHAPTER F. A. PALEY Fcap Fellow of St Fellow of Trinity Geometrical given angle given ratio Greek Hence J. R. SEELEY J. W. DONALDSON JONATHAN PALMER Late Fellow less than 90 log(s loga logarithms M.A. Fellow Mathematics negative and decreases P'OM Pembroke College perpendicular positive angle prove r₁ radius recensuit right-angled triangles POM secA secant Second Edition sides sin²A sin³A sinA sinB sine sine and cosine solution solve the triangle St John's College Students subtended subtract tanA tangent triangle ABC TRIGONO Trigonometrical Ratios Trinity College University of Cambridge values W. H. BESANT ОР
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