Question

the period of sin x/cos3x +sin3x/cos9x + sin9x/cos27x + sin27x/cos81x is

the options are÷
1. 2π/3
2. π/81
3. 2π
4. π​

Answer 1

Answer:

sinx/cos3x + sin3x/Cos9x +sin9x/cos27x +sin27x/cos81x = 0

or sinxcosx/cos3xcosx + sin3xcos3x/Cos9xcos3x +sin9xcos9x/cos27xcos9x +sin27xcos27x/cos81xcos27x = 0

or sin2x/cos3xcosx + sin6x/Cos9xcos3x +sin18x/cos27xcos9x +sin54x/cos81xcos27x = 0

or sin(3x-x)/cos3xcosx + sin(9x-3x)/Cos9xcos3x +sin(27x-9x)/cos27xcos9x +sin(81x-27x)/cos81xcos27x = 0

0r tan3x -tanx + tan9x-tan3x + tan27x -tan9x + tan81x -tan27x =0

tan81x - tanx =0

tan81x = tanx

81x = kπ + x

x = kπ/80 where k is any intiger