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Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that:
$\tan\frac{5\pi}{4}\cot\frac{9\pi}{4}+\tan\frac{17\pi}{4}\cot\frac{15\pi}{4}=0$
✓

Answer

$\text{L.H.S}=\tan\frac{5\pi}{4}\cot\frac{9\pi}{4}+\tan\frac{17\pi}{4}\cot\frac{15\pi}{4}$
$=\tan225^\circ\cot405^\circ+\tan765^\circ\cot675^\circ$
$=\tan\Big(\pi+\frac{\pi}{4}\Big)\cot\Big(2\pi+\frac{\pi}{4}\Big)+\tan\Big(4\pi+\frac{\pi}{4}\Big)\cot\Big(4\pi-\frac{\pi}{4}\Big)$
$=\tan\frac{\pi}{4}\cot\frac{\pi}{4}+\tan\frac{\pi}{4}\Big(-\cot\frac{\pi}{4}\Big)$
$=1.1+1.(-1)$
$=1-1$
$=0$
$=\text{R.H.S}$
$\text{Proved}$

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