Plane trigonometry, by S.L. Loney.

XX

TRIGONOMETRY.

2sin a cosh / - i cos a sinh /3
cosh 2/3- cos 2a
20. 2cos a cosh / + i sin a sinh/3
cos 2a + cosh 2/3
21. sinh a cos/3 + i cosh a sin 3.
sinh 2a + i sin 2,/
cosh 2a + cos 2,3
cosh a cos -i sinh a sin /3
cosh 2a + cos 2/3
LVI. (Page 381.)
r i 1 + sin O
1. + + log + s — ii, according as cos 0 is positive or
- 4 4 + 1 - sin,
negative.
2. sin-l (^/sin f) + i log [/s1 i + sin 0].
LVII. (Page 388.)
1 v
15. 2 log (u2 + v2)+ i tan-l v, where
1 cosh 2yt- cos 2xwher
=1 cosh 2y- cos 2 and v = tan-' (cot x tanh y).
2
LIX. (Pages 402, 403.)
1. 3. 2. 2. 3. 5. 4. -1. 5. -3.
LX. (Pages 407, 408.)
4 sin a
5 -4 cos a
2. 0, provided a does not equal a multiple of 7r.
sin2a 4. sin a (cos a- sin a)
1 - sin 2a + sin2 a 1 - sin 2a + sin2 a
5 sin a-c sin (a —/3)-cnsin (a + /) )c + lsin {a+ (n- 1)/
- 2c cos 3 + c2
sin a - c sin (a - 3)
1-2ccos p + c2