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If T n = (sin n x + cos n x ), then the permissible values of x , (T 5 --T 3 ) ​​/ (T 7 --T 5 ) is always equal to ...

If Tn = (sinnx + cosnx), then the permissible values of x, (T5--T3 ) ​​/ (T7--T5) is always equal to ...

Grade:11

1 Answers

Lab Bhattacharjee
121 Points
6 years ago
\text{For } m\ge3,\\ T_{m+2}-T_m=\sin^{m+2}x+\cos^{m+2}x-(\sin^mx+\cos^mx)\\ =\sin^mx(\sin^2x-1)+\cos^mx(\cos^2x-1)\\ =-\sin^2x\cos^2x(\sin^{m-2}x+\cos^{m-2}x)

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