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Question

# Which of the following is/are correct regarding their fundamental period?

A
1|sinx|+|cosx|π/2
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B
|sinx+cosx|π
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C
|sinx+cosx|+|sinxcosx|3π/2
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D
|sinx|cosx+sinx|cosx|2π
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Solution

## The correct option is D |sinx|cosx+sinx|cosx|→2πIf f(x), g(x) are complementary even functions, then period of f(x)±g(x) is 12(L.C.M of period of f(x), period of g(x)) And |sinx|,|cosx| are complementary function. (a) We know that the fundamental period of |sinx| and |cosx| is π. Now, the period of |sinx∣+∣cosx∣→12(L.C.M(π,π))=π2​ So, the period of 1|sinx|+|cosx|→π2 (b) |sinx+cosx|=√2|sin(45°+x)| So, the period of √2|sin(45°+x)| is π, Therefore, the period of |sinx+cosx|→π (c) The period of |sinx±cosx| is π. ∵|sinx+cosx∣+∣sinx−cosx| are complementary functions​. ∴ Period of |sinx+cosx∣+∣sinx−cosx∣ =12(L.C.M(π,π))=π2 (d) Period of |sinx|cosx=L.C.M.(π,2π)=2π Period of sinx|cosx|=L.C.M.(2π,π)=2π ∴ Period of |sinx|cosx+sinx|cosx|=L.C.M.(2π,2π)=2π

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