Plane trigonometry, by S.L. Loney.

[Exs. XVIII.]

EXAMPLES.

125

A A
A 2/i sin A I d 1 + sin A, when A,
25. 2cos — = - = sin sin - when -140~.
26. If A =340~, prove that
2 sin 2 1 +sin + /1 -- sin A,
and 2 o 2 - hel+sin A-1-sin.
27. If A _460~, prove that
2cos = - a/1+ sin A+ /1 sinA.
28. If A=580~, prove that
2sin = - Jl+sinA - l - sin A.
29. Within what respective limits must 2 lie when
(1) 2sin-= 1/l+sinA +/1- sin A.
(2) 2sin = - ^/1+ sin A + /1- sin-A,
(3) 2sin.=4 +l+sinA- J1-sinA,
(3) 2 sin A-+ V1 + sin A - 1 - sin A,
and (4) 2cos2= A /1+sinA - 1 -sinA.
30. In the formula
A
2 cos = A /1 + sin A 4fi /1 -sin A,
find within what limits - must lie when
(1) the two positive signs are taken,
(2) the two negative,,,,
and (3) the first sign is negative and the second positive.
31. Prove that the sine is algebraically less than the cosine for any
37r where is ay iteger.
angle between 2n7r- and 2nmr + where n is any integer.
4 4