Prove that cos- 5 -cos 2- 5 - 1 2

According to given question,Solving LHS, cosπ5 cos2π5 √(5)+14 √(5) 14 14+14 12 =RHS,Hence proved #160; ...

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Prove that ...

Question

Prove that $cos \frac{π}{5} - cos \frac{2 π}{5} = \frac{1}{2}$

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cos \frac{π}{5} + cos \frac{2 π}{5} + cos \frac{6 π}{5} + cos \frac{7 π}{5}

θ

c o s θ = \frac{8}{17},

c o s (\frac{π}{6} + θ) + c o s (\frac{π}{4} - θ) + c o s (\frac{2 π}{3} - θ)

= (\frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}}) \frac{23}{17}

cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7} = - \frac{1}{2}

c o s \frac{2 π}{7} c o s \frac{4 π}{7} c o s \frac{6 π}{7} = \frac{1}{8}

c o s \frac{π}{11} c o s \frac{2 π}{11} c o s \frac{3 π}{11} c o s \frac{4 π}{11} c o s \frac{5 π}{11} = \frac{1}{32}

Prove that : $c o s \frac{π}{5} c o s \frac{2 π}{5} c o s \frac{4 π}{5} c o s \frac{8 π}{5} = - \frac{1}{16}$

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