Plane trigonometry, by S.L. Loney.

EXAMPLES.

361

EXAMPLES. LIII.
1. Prove that
(x -2cos) (x-2cos (x - 2 cos) - 2 cos285)
= x4 +2x3 -x2 - 2x+ 1.
2. Prove that the roots of the equation
8xs + 4x2 - 4x - = 0 are cos, cos7, and cos.
27r 47r 87r
3. Prove that sin -r, sin - and sin - are the roots of the equation
7 77 7
X3 - x2 + /=.
2 8
Prove that
1 1 1
4. 4w-+ 6=1
4-sec2- 4-sec2 4-sec2 -7 7 7
7r 2f 3?r 47r 19
5. c4 + cos4 +cos4 + cos4 1.
9 9 9 9 16'
6. sec4 = + sec4 2 + ec4 + sec4 = 1120.
s9 4 9 9 9+
7r 3w 57 77 9w 1
7. cos- + cos -- + c os i- + c os + cos = '
11 11 11
8. Form the equation whose roots are
ta.2 7r 22r 37r 47r 57r
tan2 1, tan2, tan2 i, tan2 and tan2.
[Commence with equation (3) of Art. 277.]
w- 2r 37r 47r 57r
9. cot2 1 + cot2 + cot2 + cot2 + ct2 - = 15.
2wr 3wr 4w 5w
10. sec2 r + sec2 1 + sec2 3 + sec2 i + seca -= 60.
Prove that
27r 6r 187r 4/13- 1
11. cos l + cos + cos = 4
COj3 13 13 4