Question

if 3 cot a=4, find the values of cosec^2 a +1/cosec^2 a -1

Answer 1

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Your answer
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$given \: that \: - \\ \\ 3 \cot(a) = 4 \\ \\ = > \cot(a) = \frac{4}{3} \\ \\ now \\ \\ \cot(a) = \: \frac{base}{perpendicular} \\ \\ so \\ \\ base = 4x \: and \: perpendicular \: = 3x \\ \\ by \: pythgoras \: theorem \: \\ \\ (base) {}^{2} + (perpendicular) {}^{2} = (hypotenuse) {}^{2} \\ \\ = > (4x) {}^{2} + (3x) {}^{2} = (hypotenuse) {}^{2} \\ \\ = > (hypotenuse) {}^{2} = 16x {}^{2} + 9x {}^{2} \\ \\ = > (hypotenuse) {}^{2} = 25 x {}^{2} \\ \\ = > hypotenuse = \sqrt{25 x {}^{2} } =5 x \\ \\ then \\ \\ cosec(a) = \frac{hypotenuse}{perpendicular} = \frac{5x}{3x} = \frac{5}{3} \\ \\ now \\ \\ \frac{(cosec) {}^{2}a+ 1)}{(cosec) {}^{2} a- 1)} \\ \\ = > \frac{ (\frac{5}{3} ) {}^{2} + 1 }{ (\frac{5}{3} ) {}^{2} - 1} \\ \\ = > \frac{ \frac{25}{9} + 1}{ \frac{25}{9} - 1} \\ \\ = > \frac{ \frac{25 + 9}{9} }{ \frac{25 - 9}{9} } \\ \\ = > \frac{34}{16}$
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