If Tn=sinn x+cosn x, prove that(i) T3-T5T1=T5-T7T3(ii) 2 T6-3 T4+1=0(i – InterviewSolution

1.	If Tn=sinn x+cosn x, prove that(i) T3-T5T1=T5-T7T3(ii) 2 T6-3 T4+1=0(iii) 6T10-15 T8+10 T6-1=0
Answer» If $T_{n} = \sin^{n} x + \cos^{n} x$ , prove that (i) $\frac{T_{3} - T_{5}}{T_{1}} = \frac{T_{5} - T_{7}}{T_{3}}$ (ii) $2 T_{6} - 3 T_{4} + 1 = 0$ (iii) $6 T_{10} - 15 T_{8} + 10 T_{6} - 1 = 0$

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