The equation whose roots are tan22-7- tan24-7- tan28-7- tan2 6-7

z = ^2 #10;θ #160; = 1 + tan^2 θ #160; = 1 + t Put #10;in (5) #160; #10; (t + 1)^3 24(t #10; + 1)^2 + ...

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Equations of the Form acosθ+bsinθ = c

The equation ...

Question

The equation whose roots are
$t a n^{2} \frac{2 π}{7}, t a n^{2} \frac{4 π}{7}, t a n^{2} \frac{8 π}{7} (= t a n^{2} \frac{6 π}{7})$

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c o s \frac{2 π}{7}, c o s \frac{4 π}{7} a n d c o s \frac{8 π}{7}

c o s \frac{2 π}{7}, c o s \frac{4 π}{7} a n d c o s \frac{6 π}{7}

c o s \frac{2 π}{4} c o s \frac{4 π}{7} c o s \frac{8 π}{7} = S_{3} = \frac{1}{8}

c o s \frac{2 π}{4} + c o s \frac{4 π}{7} + c o s \frac{8 π}{7} = S_{1} = - \frac{1}{2}

s e c \frac{2 π}{7}, s e c \frac{4 π}{7}, s e c \frac{8 π}{7} (= s e c \frac{6 π}{7})

c o t^{2} \frac{2 π}{7}, c o t^{2} \frac{4 π}{7}, c o t^{2} \frac{8 π}{7} (= c o t^{2} \frac{6 π}{7})

7 + \sqrt{3}

7 - \sqrt{3}

\frac{tan^{2} \frac{π}{7} + tan^{2} \frac{2 π}{7} + tan^{2} \frac{3 π}{7}}{cot^{2} \frac{π}{7} + cot^{2} \frac{2 π}{7} + cot^{2} \frac{3 π}{7}}

{tan}^{2} \frac{π}{7} + {tan}^{2} \frac{2 π}{7} + {tan}^{2} \frac{3 π}{7}

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