 | William Chauvenet - Geometry - 1896 - 274 pages
...cos J (z -f у) sin J (z — у) cosec z - cosec у = - - 8Ín z sin y - ¿ <] 82-' These formula;, although generally omitted in treatises on trigonometry,...and of (38) and (39), are sin (x + y) sin (x — y) = sin2 x cos2 y — cos2 x sin2 y cos (x + y) cos (x — y) = cos2 x cos2 «/ — sin2 x sin2 y By... | |
 | Webster Wells - Trigonometry - 1896 - 240 pages
...~~ 2 cos £ (x + y) sin $(x — y) = tan £ (z + у) cot £ (z — у) 47. By (9) and (il), we have sin (x + y) sin (x — y) = (sin x cos y + cos x sin y) (sin x cos y — cos x sin y) = sin2 x cos2 y — cos2 x sin2 у = sin2 x (1 — sin2 y) — (1... | |
 | Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 248 pages
...To prove the relation tan (i + y) = ^- —• (13) We have . tan x + tan y ,. ON 1 - tanx ten y tan (x + y) = -. ** = : :— sin (x + y) sin x cos y + cos x sin y ' cos (x + y) cos x cos y — sin x sm y sin x cos y cos x sin y cos x cos y cos x cos y tan x +... | |
 | Albert Irvin Frye - Civil engineering - 1913 - 1698 pages
...sin £ (tf + y) cos 1 cos *-f-cos y = 2 cos — y). — y). Functions of the difference of two angles (x — y). sin (x — y) = sin x cos y — cos x sin y. cos (re — y) = cos x cos y + sin # sin y. tan* — tan y cot x cot y + 1 coty-cot^ ' =• 2 cos... | |
 | George Wentworth - Plane trigonometry - 1914 - 348 pages
...increased by 90°. It is therefore true for all angles. , Similarly, by § 87, cos (x' + y) = cos (90° + x + y) = — sin (x + y) = — sin x cos y — cos x sin y = cos x' cos y — sin ж' sin y, by substituting cos x' for — sin x and sin x' for cos x as above.... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...95. Tangent of the Sum of two Angles. rived from the addition formulas as follows This can be detan (x + y) = sin (x + y) sin x cos y + cos x sin y cos (x + y) cos x cos y — sin x sin y ' If we divide each term of the numerator and denominator... | |
 | Mechanical engineering - 1924 - 738 pages
...cos ( — x) -= cos x; tan ( — x) = — tan x. Functions of the Sum and Difference of Two Angles. sin (x + y) = sin x cos y + cos x sin # ; cos (x + 2/) = cos x cos y — sin x sin y ; tan (x + y) - [tan x + tan j/]/[l — tan x tan y]; cot (x +... | |
 | Dynamics - 1010 pages
...equation for it does not equal zero, and, accordingly, it is not a possible velocity potential. (d) f = sin (x + y) sin (x + y) = sin x cos y + cos x sin y 32f _ 32 (sin x cos y + cos x sin y) 3x2 3x2 = - sin x cos y - cos x sin y 32f __ 92(sin x cos y... | |
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I sin y \2 / \2 / = sin x cos y + cos x sin y, sin (a; — y) = sin (x + (— y)) = sin a; cos (— y) + cos a; sin (— y) = sin x cos y — cos x sin y, tan (x + y) = sin (x + y) sin x cos y + cos x... 