| Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...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
...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.... | |
| Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 366 pages
...the third side when two sides and 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... | |
| William Charles Brenke - Trigonometry - 1917 - 200 pages
...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... | |
| Leonard Magruder Passano - Trigonometry - 1918 - 330 pages
...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** opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A... | |
| Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...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** opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A... | |
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