(17) sin (0+ a) sin a =cos 0+cot a sin 0; use this transformation in Ex. (8), expand cos + cot a sin 0 in ascending powers of 0 by Art. 41 and equate the coefficients of 0 on each side. (19) This result may be deduced from Ex. (13). (20) Put π-a for a in (19). (1) (i) 2 cos 40o, 2 cos 160o, 2 cos 80o. (ii) √2 cos 15o, 2 cos 135°, √2 cos 105°. (iii) 2 cos 40° +1, 2 cos 160° +1, 2 cos 80° +1. (iv) 2/2 cos 45°-4, 2√2 cos 1650 - 4, 2/2 cos 75° - 4, (v) (2) (i) 4 cos 10°-√3, 4 cos 130°/3, 4 cos 110o-/3. (iii) 3a=74°55′47′′. (3) (i) Find a and ẞ such that a=tan a, b=tan ß, then (ii) a+b=sin (a±ẞ) sec a sec ß. a cos 0±b sin 0=a cos (0 = a) sec a, where tan a== (iii) 4 sin (B+ C) sin (C+A) sin § (A+B). (iv) 4 sin (0 – a) sin (m) − a) cos (0 – ma). (v) 4R sin A sin B sin C. XLI. (2) Divide the first equation by a, the second by b, square both sides and add. (9) cos 40=3(2m2 - 5), sin (a−40) = 1 sin a, and so on. (85) π3. XLIII. (91) sin is greater than 0 – 103, when 0 is less than π cos is less than 1-102+04. [Art. 44, 45.] VII. 4. {cos (a+B+y) + cos 1 (B+y− 3a) + cos § (y+ a −38) +cos(a+ẞ-3y)}. 9. (1) ee-mx cos (e e-mx sin nx); (2) cos {a+(n+1)ẞ} sin nẞcosec ß. 10. г+-{x ̄1- x ̄2 (sin a)−2 sin 2a + 3x ̃3 (sin a)−3 sin 3a — ...}. CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. & SON, AT THE UNIVERSITY PRESS. A CATALOGUE OF 'CLASSICAL WORKS PUBLISHED BY MACMILLAN AND CO., LONDON, COMPRISING 1. ELEMENTARY CLASSICS, for Beginners. 2. THE CLASSICAL SERIES, for Schools and Colleges. 3. THE CLASSICAL LIBRARY, for Higher Students (a) TEXTS; (b) TRANSLATIONS. 4. WORKS ON GRAMMAR, COMPOSITION, & PHILOLOGY. 5. WORKS ON ANTIQUITIES, ANCIENT HISTORY, ANCIENT PHILOSOPHY. |