<prompt> Kwa nambari kamili n, 0  <response>: Kumbuka hiloanzaaligncot x - cot 2x fraccos xsin x - fraccos 2xsin 2x frac2 cos2 x2 sin x cos x - frac2 cos2 x - 12 sin x cos x frac12 sin x cos x frac1sin 2x csc 2x.endalignKwa hivyo, muhtasari wa x 22circ, 23circ, 24circ, dots, 22018circ, tunapataanzaaligncsc 23circ csc 24circ csc 25circ dots csc 22019circ kitanda 22circ - kitanda 23circ kitanda 23circ - kitanda 24circ cot 24circ - cot 25circ dots cot 22018circ - cot 22019 mduara cot 4circ - cot 22019circ.endalignKumbuka kwamba 214 equiv 22 pmod180, so22019 equiv 22007 equiv 21995 equiv dots equiv 215 equiv 32768 equiv 8 pmod180,so cot 22019circ cot 8circ. Kisha kitanda 4circ - cot 8circ csc 8circ sec 82circ,hivyo n 82. 