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B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Elements of Geometry and Trigonometry - Page 225
by Adrien Marie Legendre - 1838 - 269 pages

A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...a (27-) = sin a sin b —cos a cos b (13.) .•. — cos (aJ-ft) = sin a sin b — cos a cos b, and cos (a + b) = cos a cos b — sin a sin b. And, in a similar manner, it may be shewn, that cos (a — b) = cos a cos b + sin a sin b. It is evident,...

Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 366 pages
...45°, shew that 2 sin ^ ± aj = \/l + cos 2a ± v/1 — cos 2a, PLANK TRIGONOMETRY. 1832 82. Prove that cos (A — B) = cos A . cos B + sin A . sin B; and find sin 3A in terms of sin A. QQ A * *2 + c2 — <*2 j . oo. Assuming cos A = ^ , deduce an expression...

Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848 - 284 pages
...their sum or difference. . sin ( A + B) sin A . cos B + cos A . sin B tan(A + B)= ) , (- = — . --. v cos (A + B) cos A . cos B — sin A . sin B and dividing numerator and denominator by cos A . cos B, sin A sin B cos A "'"cos B tan A + tan B 1 tan...

Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...it would still follow that cos (a + b) = CK'—I'L', or R cos (a + b) = cos a cos b—sin a sin h. And whatever be the values of the arcs a and b, it...formulas for the purpose of more convenient reference. sin a cos £ + sin b cos a sin ' . , ,, sin a cos b—sin b cos a ,_ > sin («—b)= g (2.). R _ cos...

Military examinations. Mathematical examination papers, set for entrance to ...

...the same sign ? Find sin 120°, tan 60°, cos 135°. т> • » Prove sin A = —= (tan A)* 3. Prove cos (A -)- B) = cos A cos B — sin A sin B, and deduce from the formula the corresponding expressions for sin ( A -f- B), sin (A — B), and cos 2A....

Plane Trigonometry for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Plane trigonometry - 1882 - 341 pages
...+ B) = sin A cos Л + cos A sin B, then cos' (A + B) = (cos A cos B - sin A sin £)', and therefore cos (A + B) - ± (cos A cos B - sin A sin .B) ; and a little consideration shews that we must take the upper sign. 327. In Chapter viii. we have given...

Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

...3. If (A + B) is an angle in the first quadrant, obtain by means of a geometrical figure the formula cos (A + B) = cos A cos B - sin A . sin B, and deduce from it the expression for cos (A — B). Find sec (A +B) in terms of sec A and sec B, and prove...

A Treatise on Higher Trigonometry

John Bascombe Lock - Trigonometry - 1884 - 208 pages
...{ - (180° + Л)}. Write down formulas including all angles which satisfy — (1) (2) 3. Prove that cos (A + B) = cos A cos B -sin A sin B, and deduce expressions for cos2Л, cos ЗA in terms of cos A. 5. Prove that (1) (2) (3) cos 20° + cos...