Plane trigonometry, by S.L. Loney.

362 TRIGONOMETRY. [Exs. LIII.]
107r 147r 227r -,/13 -1
12. cos + cos3 + cos 3 = —
1 3 1 3 L 4
r 77r 11r 137r 1
13. cos - + c os -- + cos-= -
15 15 15 15 2
14. Prove that sin 7r is a root of the equation
64x6 - 804 + 24x2 - 1 = 0.
Find the value of
15. os cos + os(+2ro ( +4r).....cos 0+(n-1)27
\ n I \ n 2n
16. insi(+ i +......sin+s 7.....sin {0+(n-l)2 t.
17. cosec2 0 + cosec2 ( + 2r) + cosec2 ( +...... to n terms.
18. tan +tan2 (+ + tan2 +..... to n terms.
[For the following 5 questions commence with equation (5) of Art.
277.]
19. tan +tan (0 +- )+tan (+-...... to n terms.
20. cot 0 +ot (0+) +cot(0+ )......to ters.
21. tan 0 tan n (+ tan O+...... to n factors.
22. tan + tan2 (0+) + tan2 ( + 2z +...... to n terms.
23. If n be odd, prove that S=3C=n2 - 1, where
S rsec2 w 2r 3w
S = s — v sec2 - + sec2 — +...... to n - 1 terms,
n n n
and = coseC- + cosec2 -- + cosec2-_ +. to n- I terms.
n n n
24. Find the sum of the products, taken two at a time, of expressions
of the form sec ( + -2rr), where r has all values from zero to n-1.
\ n ]