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Trigonometric Functions — MATHS STD 11 Science — Question

Gujarat 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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