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  4. The value of cot((π/4)+θ)cot((π/4)-θ) is

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Q. The value of $cot\left(\frac{\pi}{4}+\theta\right)cot\left(\frac{\pi}{4}-\theta\right)$ is

Trigonometric Functions

Solution:

Given, $cot\left(\frac{\pi}{4}+\theta\right)cot\left(\frac{\pi}{4}-\theta\right)$
$=\frac{cot \frac{\pi}{4}cot\,\theta-1}{cot \frac{\pi}{4}+cot\,\theta}\times \frac{cot \frac{\pi}{4} cot\,\theta+1}{cot\,\theta-cot \frac{\pi}{4}}$
$=\frac{cot\,\theta-1}{1+cot\,\theta} \times \frac{1+cot\,\theta}{cot\,\theta-1}=1$