Question
Very-Short and Short-Answer Qustions:
Write the value of $\sin^2\theta\cos^2\theta\big(1+\tan^2\theta\big)\big(1+\cot^2\theta\big)$
Write the value of $\sin^2\theta\cos^2\theta\big(1+\tan^2\theta\big)\big(1+\cot^2\theta\big)$
✓
Answer
$\sin^2\theta\cos^2\theta\big(1+\tan^2\theta\big)\big(1+\cot^2\theta\big)$
$=\sin^2\theta\times\cos^2\theta\times\sec^2\theta\times\text{cosec}^2\theta$
$=\sin^2\theta\times\cos^2\theta\times\frac{1}{\cos^2\theta}\times\frac{1}{\sin^2\theta}$
$=1$
$=\sin^2\theta\times\cos^2\theta\times\sec^2\theta\times\text{cosec}^2\theta$
$=\sin^2\theta\times\cos^2\theta\times\frac{1}{\cos^2\theta}\times\frac{1}{\sin^2\theta}$
$=1$
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