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Trigonometric Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that: $\frac{\cos(2\pi+\text{x})\text{cosec}(2\pi+\text{x})\tan\Big(\frac{\pi}{2}+\text{x}\Big)}{\sec\Big(\frac{\pi}{2}+\text{x}\Big)\cos\text{x}\cot(\pi+\text{x})}=1$
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Answer

$\text{L.H.S}=\frac{\cos(2\pi+\text{x})\text{cosec}(2\pi+\text{x})\tan\Big(\frac{\pi}{2}+\text{x}\Big)}{\sec\Big(\frac{\pi}{2}+\text{x}\Big)\cos\text{x}\cot(\pi+\text{x})}$ $=\frac{\cos\text{x}\times\text{cosec }\text{x}(-\cot\text{x})}{-\text{cosec }\text{x}.\cos\text{x}\cot\text{x}}$ $\begin{pmatrix}\because\tan\Big(\frac{\pi}{2}+\text{x}\Big)=-\cot\text{x}\\\&\sec\Big(\frac{\pi}{2}+\text{x}\Big)=-\text{cosec}\text{x}\end{pmatrix}$ $= 1$ $= \text{R.H.S}$ $\text{Proved}$

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