MHB Number of Real Solutions for Trigonometric Equation

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The equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$ is analyzed for real solutions within the interval $0 \leq x \leq 2\pi$. The discussion concludes that there are exactly two real solutions to this equation. Participants explore the behavior of the sine and cosine functions, emphasizing their periodic nature and the implications for the number of intersections. The analysis highlights the complexity of nested trigonometric functions and their impact on solution counts. Ultimately, the consensus is that the equation yields two distinct solutions in the specified range.
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Number of real solution of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$

where $ 0 \leq x\leq 2\pi$
 
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jacks said:
Number of real solution <--- 2
of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$

where $ 0 \leq x\leq 2\pi$

...
 

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