Question
Very-short and Short-Answer Questions.
Write the value of $\text{cosec}^2\theta(1+\cos\theta)(1-\sin\theta).$
Write the value of $\text{cosec}^2\theta(1+\cos\theta)(1-\sin\theta).$
✓
Answer
$\text{cosec}^2\theta(1+\cos\theta)(1-\sin\theta)$$=\text{cosec}^2\theta\big(1-\cos^2\theta\big)$
$=\text{cosec}^2\theta\times\sin^2\theta$
$=\frac{1}{\sin^2\theta}\times\sin^2\theta$
$=1$
$=\text{cosec}^2\theta\times\sin^2\theta$
$=\frac{1}{\sin^2\theta}\times\sin^2\theta$
$=1$
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