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Mathematics Question on Trigonometric Equations

The period of function f(x) = elog(sinx)+(tanx)3−cosec(3x−5)e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)is

A

π

B

π/2

C

2π

D

2π/3

Answer

2π

Explanation

Solution

The correct option is (C) 2π.

The periodicity of the trigonometric functions involved in the expression needs to be considered. The periods of sin x , tan(3 x), and csc(3 x −5) are 2 π , and π ​ and 2 π ​/3 respectively.

Hence, the period of f(x) is determined by the least common multiple (LCM) of 2 π , π , and 2 π ​/3, which is 2 π.