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Trigonometric Ratios of Multiples of an Angle

If Tn=sin^n x...

Question

If Tn=sin^n x + cos^n x, prove that- T3 - T5/T1 = T5 - T7/T3

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t_{n} = {sin}^{n} θ + {cos}^{n} θ

, then prove that

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

T_{n} = {sin}^{n} θ + {cos}^{n} θ

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

T_{n} = s i n^{n} θ + c o s^{n} θ

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

T_{n} = {sin}^{n} x + {cos}^{n} x

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

T_{n} = {sin}^{n} θ + {cos}^{n} θ

\frac{_{3} - T_{5}}{T_{1}} \neq \frac{T_{5} - T_{7}}{T_{3}}

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