Plane trigonometry, by S.L. Loney.

130

TRIGONOMETRY.

[Exs. XIX.]

3. cos 12~ + cos 60~ + cos 84~ = cos 24~ + cos 48~.
7r. 2. 3r. 47r 5
4, sin5 sin sin s sin = 16
-. 13r 1. 7. 137 1
5. sin si- + sin 2 6. sin j- sml 4
7. tan 6~ tan 42~ tan 66~ tan 78~ = 1.
7r 27 37r 47r 57r 6r 77r 1
8. cos -5 cos cos i- cos i- cos 5 cos i5 cos 1-5 = 27.
27 47 87r 147r
9. 16c os j cos - c 5 os - 1.
10. Two parallel chords of a circle, which are on the same side of the
centre, subtend angles of 72~ and 144~ respectively at the centre. Prove
that the perpendicular distance between the chords is half the radius of
the circle.
11. In any circle prove that the chord which subtends 108~ at the
centre is equal to the sum of the two chords which subtend angles of 36~
and 60~.
12. Construct the angle whose cosine is equal to its tangent.
13. Solve the equation
4 cos 0 - 3 sec 0=2 tan 0.