Prove that t 7 1 - t 2 - t 5 - t 3 - t - t 1 - t 2

P.T t^71 + t^2 = t^5 t^3 + t t1 + t^2 t^7 + t^5 t^5 + t^3 t^3 + t t1 + t^2 = t^71 + t^2 t^5 (1 + t^2) t^3 (1 + t^2) + t(1 + t^2) t1 + ...

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(a-b)^2 Expansion and Visualisation

Prove that ...

Question

Prove that
$\frac{t^{7}}{1 + t^{2}} = t^{5} - t^{3} + t - \frac{t}{1 + t^{2}}$

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S_{1} = T_{1} + T_{2} + T_{3} + \dots + T_{n}

S_{2} = T_{1} + T_{3} + T_{5} + \dots + T_{n}, t h e n S_{1} / S_{2} =

S_{1} = T_{1} + T_{2} + T_{3} +

+ T_{n}

S_{2} = T_{1} + T_{3} + T_{5} +

+ T_{n}

S_{1} / S_{2} =

t_{0}, t_{1}, t_{2}, t_{n}

(x + a i)^{n}

(t_{0} - t_{2} + t_{4} - t_{6} + \dots .)^{2} + (t_{1} - t_{3} + t_{5} \dots .)^{2} =

T_{n} = {sin}^{n} θ + {cos}^{n} θ

\frac{T_{3} - T_{5}}{T_{1}} = \frac{T_{5} - T_{7}}{T_{3}}

S_{1} = T_{1} + T_{2} + T_{3} + . . . + T_{n}

[n

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S_{2} = T_{1} + T_{3} + T_{5} + . . . + T_{n}

\frac{S_{1}}{S_{2}} =

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