PLANE TRIGONOMETRY. 85 



A cos 30 cos 50 



(12) cos0- + - -- ...to oo, 



O O 



(13) COS7^ + 7lCOs(H-l)d + ^^^COs(7l- 



A cos 20 cos 3d 

 (H) cos0-- - - + _ -- ...to oo, 



- 1 cos 30 1.3 cos 50 

 (1.,) oo. + I _3_ + j-^ -_+... toco, 



(16) costfsinfl + cos'e + cos'tfH.... to oo, 



cos'20 cos 30 1.3 ^00850 

 (17) cos20cos0 + - + cos 3 20 _+... to oo. 



a o . 4 



399. Prove that 



sec + sec( + 0) + sec ( + 0} -f- ... + sec (^(m -1)- + 0) 

 V/t / \w* / ( v 'm ) 



m-l 



nil to 0, or to (- 1) T sec 7>i0, according as m is even or 

 odd: also that 



is equal to ^ , or to m* see 1 wi0, according as ;/i is 

 1 -(-!)' cos mB 



or odd. 



400. Prove that 



n .sin ?<^ tin^ gin <fr 



i 1 1 < /, sin 



