Plane trigonometry, by S.L. Loney.

TRIGONOMETRY.

Hence QT= 2PS, and RT = 2RS, i.e. MN = 2ML.
Therefore MQ + NR = TQ + 2LS= 2SP + 2LS= 2LP.
Also OM + 0O = 20M + MN = 20M + 2ML = 20L.
MQ N MQ+ NR
Hence sin C +sin D =Q +R=
0Q ORQ OR
C
/O/D
/T ' PsR
0 M L N A
2LP LPOP
-=2 2sin LOPcosPOR
OR OPOR
C+D C-D
=2 sin - cos
2 2
Again sin C- sin D = - _ MQ-NR
OQ OgR - OR
SP SP RP
= 2=2- 2 cosSPR sinROP
OR RPO' R
C+D. C-D
= 2 cos - sinl
2 2
[ for zSPR=90-Oz SPO = LOP= C+ D]
OM ON OM+ ON
Also cos C + cos D = + OR- -
OQ OR OR
OL OL OP
=2 R=2 -OR
0R o OP OR
C+D C-D
=2 cos LOP cos POR = 2 cos cos
2 2