 | Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...solution by logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. „ „ a sin a: f . ,, Proof. T = - —... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...solution by logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. a sina Proof. r = -. — -, from sine theorem.... | |
 | William Charles Brenke - Trigonometry - 1917 - 194 pages
...other two sides minus twice their product by the cosine of their included angle. Law of Tangents. — The sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Half Angles. — The sine of half an angle... | |
 | John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...+ b : a — b : : tan. r (A + B) : tan. X (A - B) 2 2 The above result may be enunciated thus— ^ The sum of two sides is to their difference as the tangent of half the sun of their opposite angles is to the tangent of half their difference. By combining the last two... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...sides arid the included angle are given. 101. Law of Tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of half their difference. From the law of sines, we have a... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 330 pages
...cannot be greater than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference...the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A : sin B.... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...cannot be greater than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference...the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A : sin B.... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 198 pages
...cannot be greater than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposlte the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A... | |
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In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. 
