Evaluate- i 1-cot- 3 1-cot- 3 ii 1-cos- 6 1-cos- 6

(i)1 π31+π3 =1 1√(3)1+1√(3) =√(3) 1√(3)+1 =√(3) 1√(3)+1×√(3) 1√(3) 1 =3+1 2√(3)3 1 =4 2√(3)2 =2 √(3) (ii)1 cosπ61+cosπ6 ...

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Trigonometric Ratios of Multiples of an Angle

Evaluate: i ...

Question

Evaluate:
$(i) ⎛ ⎜ ⎜ ⎝ \frac{1 - c o t \frac{π}{3}}{1 + c o t \frac{π}{3}} ⎞ ⎟ ⎟ ⎠$
$(i i) \frac{1 - c o s \frac{π}{6}}{1 + c o s \frac{π}{6}}$

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Solution

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{⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{sin \frac{π}{6} + i (1 - cos \frac{π}{6})}{sin \frac{π}{6} - i (1 - cos \frac{π}{6})} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{3}

i = \sqrt{- 1}

{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{6} - i sin \frac{π}{6}}{1 + cos \frac{π}{6} + i sin \frac{π}{6}} ⎞ ⎟ ⎟ ⎠}^{6}

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{(\frac{1 + c o s \frac{π}{8} - i s i n \frac{π}{8}}{1 + c o s \frac{π}{8} + i s i n \frac{π}{8}})}^{8}

{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}

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