Question : Simplify the following: $\mathrm{(1+cot^2\theta)(1-cos\theta)(1+cos\theta)}$
Option 1: 1
Option 2: –5
Option 3: 3
Option 4: –3
Correct Answer: 1
Solution : $\mathrm{(1+cot^2\theta)(1-cos\theta)(1+cos\theta)}$ $=\mathrm{(1+cot^2\theta)(1-cos^2\theta)}$ $=\mathrm{(cosec^2\theta)(sin^2\theta)}$ $=1$ Hence, the correct answer is 1.
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