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In any plane 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.
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 405
by Charles Butler - 1814

## Mathematics for Collegiate Students of Agriculture and General Science

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...

## A Complete Epitome of Practical Navigation, and Nautical Astronomy ..., Volume 1

John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...— 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...

## Plane and Spherical Trigonometry

Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...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 opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A...