Wentworth, G. A. (George Albert), 1835-1906 · Boston, Ginn & company · leaf 52
= cosx X OF = cosx cosy. OF J T)C = sin x; hence, FG = sin a; X CD = sin# siny. Therefore, cos(x + y) = cos x cos y — sinx siny. [5] In this proof x and y, and also the sum x -f- y, are assumed to be acute angles. If the sumx-\~y of the acute angles a? andy is obtuse, as in Fig. 28, theproof… … 44 TRIGONOMETRY. If these formulas hold true for any two acute angles x andy, they hold true when one of the angles is increased by 90°.Thus, if for x we write x = 90° + x, then, by § 29, sm(V-fy) = sin(90° -f- x + y) = cos(#+ ;?/),c<as(V-f- y) = cos (90° -f x -f y) = — sin (# + y)- Hence, by…
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