While attempting to verify the identity 1- ^2 =

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

While attempting to verify the identity 1−cos⁡2θsin⁡θ=sin⁡θ,\frac{1-\cos^2\theta}{\sin\theta}=\sin\theta, a student writes: Step 1 1−cos⁡2θsin⁡θ=sin⁡2θsin⁡θ\displaystyle \frac{1-\cos^2\theta}{\sin\theta}=\frac{\sin^2\theta}{\sin\theta} Step 2 sin⁡2θsin⁡θ=cot⁡θ\displaystyle \frac{\sin^2\theta}{\sin\theta}=\cot\theta (for sin⁡θ≠0\sin\theta\ne0). Which step is incorrect? Rewrite that step correctly.

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