What is the range of sinx and cosx?
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As the domain of sinx as well as cosx is (-∞,∞), thus the domain of the funtion f(x) will the the intersection of the two domains which comes out to be (-∞,∞) that is, that x can take any real value ranging from -∞ to +∞. Therefore, the domain is (-∞,+∞).
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