Question

If tan theta = 1/root3.evaluate cosec^2 theta - sec ^2 theta ÷ cosec^2 theta + sec^2 theta

Answer 1

Answer:

$value \:of \\\frac{cosec^{2}\theta-sec^{2}\theta}{cosec^{2}\theta+sec^{2}\theta}=\frac{1}{2}$

Step-by-step explanation:

$Given\:tan\theta = \frac{1}{\sqrt{3}}$

$\implies tan\theta = tan30\degree$

$\implies \theta = 30\degree\:---(1)$

$Now , \: value \:of \\\frac{cosec^{2}\theta-sec^{2}\theta}{cosec^{2}\theta+sec^{2}\theta}\\=\frac{cosec^{2}30\degree-sec^{2}30\degree}{cosec^{2}30\degree+sec^{2}30\degree}\\=\frac{4-\frac{4}{3}}{4+\frac{4}{3}}\\=\frac{\frac{12-4}{4}}{\frac{12+4}{4}}\\=\frac{12-4}{12+4}\\=\frac{8}{16}\\=\frac{1}{2}$

Therefore,

$value \:of \\\frac{cosec^{2}\theta-sec^{2}\theta}{cosec^{2}\theta+sec^{2}\theta}=\frac{1}{2}$

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Answer 2

hope that this will help you