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if:f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(...

if:`f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(sqrt(1+cot^2x)),` then find the range of `f(x)`

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To find the range of the function \( f(x) = \frac{\sin x}{\sqrt{1 + \tan^2 x}} - \frac{\cos x}{\sqrt{1 + \cot^2 x}} \), we can simplify the expression step by step. ### Step 1: Simplify the terms We know from trigonometric identities that: - \( 1 + \tan^2 x = \sec^2 x \) - \( 1 + \cot^2 x = \csc^2 x \) Thus, we can rewrite the function as: ...
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