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Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM rule we get π/6 but π/12 gives you same value as π/6.?
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Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM r...


Period of the Function

The period of a function is the smallest positive value of T for which f(x+T) = f(x) for all x. In this case, we are looking for the period of the function f(x) = (sin12x)/(1-cos^2(6x)).

Using Trigonometric Identities

We can simplify the function using trigonometric identities. Note that cos^2(θ) = 1 - sin^2(θ). Therefore, the function can be rewritten as f(x) = sin(12x) / sin^2(6x).

Period of sin(ax)

The period of sin(ax) is 2π/a. In this case, the period of sin(12x) is 2π/12 = π/6.

Period of sin^2(ax)

The period of sin^2(ax) is π/a. In this case, the period of sin^2(6x) is π/6.

Final Period Calculation

Since the period of sin(ax) is π/6 and the period of sin^2(ax) is also π/6, the period of the function f(x) = (sin12x)/(1-cos^2(6x)) is the LCM of the periods, which is π/6.

Conclusion

Therefore, the period of the function f(x) = (sin12x)/(1-cos^2(6x)) is π/6.
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Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM rule we get π/6 but π/12 gives you same value as π/6.?
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Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM rule we get π/6 but π/12 gives you same value as π/6.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM rule we get π/6 but π/12 gives you same value as π/6.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find period of `f(x)=(sin12x)/(1 cos^(2)6x)` My ans( π/12) as by LCM rule we get π/6 but π/12 gives you same value as π/6.?.
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