 | Robert Woodhouse - Plane trigonometry - 1819 - 300 pages
...subtracting (l>) and (c), there will result sin. (A — B)= sin. A . cos. B — cos. A . sin. B, and sin. (A + B) = sin. A . cos. B + cos. A . sin. B, and the deduction of other forms from these fundamental ones may be conducted as it is in the text. Mr.... | |
 | Mathematics - 1836 - 366 pages
...and prove that it is an incommensurable quantity. 1834 102. Define the sine and cosine of an angle ; prove that sin (A + B) — sin A . cos B + cos A . sin B ; and write down a general formula for all angles whose cosine = — cos A . 103. Express the cosine of half... | |
 | John Martin Frederick Wright - Conic sections - 1836 - 278 pages
...of Sines as invented by Euler, the former systems of trigonometry not containing even the theorems sin. (A + B) = sin. A . cos. B ¿ cos. A sin. B, and cos. (A 4; B) = cos. A cos. B ip sin. A sin. B ; then Woodhouse's Treatise on Analytical Calculation... | |
 | John Charles Snowball - 1837 - 322 pages
...Art. 27. (5). cosec A 2 (cosec A)2- 2 .-. cos 2 A = 1 -- = - - - - . (cosec A)" (cosec Af 50. Since, sin (A + B) = sin A . cos B + cos A . sin B, and, sin (A - B) = sin A . cos B - cos A . sin B ; .-. by adding and subtracting, we have sin(^í + B) +... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...the cosine of twice the angle. Find the values of the tangent, secant, and cosecant, of 22° 30'. 10. Prove that sin (A + B) = sin A cos B + cos A sin B, and deduce a similar expression for cos (A + B). If a tan A + b tan B = (a + b) tan , shew that H a cos A b cos... | |
 | London univ - 1852 - 358 pages
...AND SPHERICAL TRIGONOMETRY. CONIC SECTIONS. Examiner, GB JERRARD, Esq. 1. Investigate the equation sin ( A +- B) = sin A cos B + cos A sin B ; and from the mode of denoting the directions of lines by their signs, show how the expressions for sin... | |
 | Thomas Percy Hudson - Trigonometry - 1862 - 202 pages
...because (A + B), A and B being each less than 90°, their sines and cosines are all positive. Hence sin (A + B) = sin A cos B + cos A sin B ; and cos (A + B) = cos A cos B — sin A sin B. Similarly, sin (A — B) and cos (A — B) may be deduced... | |
 | Samuel H. Winter - 1867 - 468 pages
...360°. (2) From tables extending from 0 to 90° how do we find the secants of angles above 90° ? 12. Prove that sin (A— B) = sin A cos B — cos A sin B; and that sin (A + 30°) + cos (A + 60°)= cos A. 13. If the sides of a triangle, 27'6 and 37'54 yds. long,... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...circular measure. 8. Define the cosine and tangent of an angle, and find those of 45°, 30°, and 60°. 9. Prove that sin (A + B) = sin A cos B + cos A sin B, and that . , . . A + B AB sin A + sin U=z sm — - — - cos — -~ — . 10. In any triangle, prove that... | |
 | John Bascombe Lock - 1882 - 378 pages
...ON . OP - NP . OP -ON' OP NP' OP =cosROE.cosEOF-ainHPN. ainEOF = cos 4 . cos B — sin 4 . sin B. To prove that sin (A - B) =sin A . cos B - cos A . sin B, and that coa(AJ])=coaA.cosB+sMA.swB. Let ROE be the angle A, and .F0.S the angle B. Then in the figure,... | |
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To prove that sin (A - B) = sin A cos B - cos A sin B, and cos (A — £) = cos A cos B + sin A sin B. 
