Plane trigonometry, by S.L. Loney.

INVERSE CIRCULAR FUNCTIONS.
12 12
Let cos-1 3=, so that cos, = 3,
and therefore sin 14 = / 1
169 13 '
16 16
Let sin-' 6=y, so that sin y=6.
We have then to prove that
a-=/y,
i.e. to shew that sin (a - p) = sin y.
Now sin (a - 3) = sin a cos 8 - cos a sin
3 12 4 5 36 - 20 16
5 *13 - 5'13 65 ~ = nSl^y.
Hence the relation is proved.
1 1wr
Ex. 2. Prove that 2 tan-1 + tan-1 =
3 7 4
1 1
Let tan-1 = a, so that tan a= 3,
3 3
1 1
and let tan-1 - =3, so that tan p =.
We have then to shew that
2a+/3=.
-~~Now tan 2a -2 tan a
Now tan 2a=_
1 - tan2 a
2
3 6 3
1-8- 4
9
Also tan (2a + } = tan 2a + tan
1 - tan2atan/3
3 1
+
4 7 21+4 25 r
= 1-ftan3 1 -28 3 25~ 4'
4'7
~7.. 2a+P3=4
I. T.

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