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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions2 Marks
Question
Prove that:
$\frac{\tan\big(\frac{\pi}{2}-\text{x}\big)\sec(\pi-\text{x})\sin(-\text{x})}{\sin(\pi+\text{x})\cot(2\pi-\text{x})\text{cosec}\big(\frac{\pi}{2}-\text{x}\big)}=1$
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Answer

$\text{L.H.S}=\frac{\tan\big(\frac{\pi}{2}-\text{x}\big)\sec(\pi-\text{x})\sin(-\text{x})}{\sin(\pi+\text{x})\cot(2\pi-\text{x})\text{cosec}\big(\frac{\pi}{2}-\text{x}\big)}$
$=\frac{\cot\text{x}\times(-\sec\text{x})\times(-\sin\text{x})}{-\sin\text{x}\times(-\cot\text{x})\times\sec\text{x}}$
$= 1$
$=\text{ R.H.S}$
$\text{Proved}$

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