If Tn - sinn - - cosn - then show that T3 - T5T1 - T5 - T7T3

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Trigonometric Ratios of Common Angles

If Tn = s...

Question

If $T_{n} = s i n^{n} θ + c o s^{n} θ$ then show that $\frac{T_{3} - T_{5}}{T_{1}} = \frac{T_{5} - T_{7}}{T_{3}}$

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T_{n} = {sin}^{n} θ + {cos}^{n} θ

\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}}

If $T_{n} = s i n^{n} θ + c o s^{n} θ$ , prove that

$(i) \frac{T_{3} - T_{5}}{T_{1}} = \frac{T_{5} - T_{7}}{T_{3}}$

$(i i) 2 T_{6} - 3 T_{4} + 1 = 0$

$(i i i) 6 T_{10} - 15 T_{8} + 10 T_{6} - 1 = 0$

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

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