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Simplify the expression (2theta)/()( - )

Mathematics

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To simplify the expression sin⁡2θsin⁡θ(csc⁡θ−cot⁡θ)\frac{\sin^2\theta}{\sin\theta}(\csc\theta - \cot\theta), we will follow these steps:

  1. Simplify the first term sin⁡2θsin⁡θ\frac{\sin^2\theta}{\sin\theta}.

    Assuming sin⁡θ≠0\sin\theta \neq 0, we can cancel one sin⁡θ\sin\theta from the numerator and denominator:

    sin⁡2θsin⁡θ=sin⁡θ\frac{\sin^2\theta}{\sin\theta} = \sin\theta

  2. Rewrite the expression with the simplified first term.

    The expression becomes:

    sin⁡θ(csc⁡θ−cot⁡θ)\sin\theta(\csc\theta - \cot\theta)

  3. Express csc⁡θ\csc\theta and cot⁡θ\cot\theta in terms of sin⁡θ\sin\theta and $\cos\theta

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