Question

cosec theta - cot theta = 5= theta lies in the quadrant​

Answer 1

Answer:

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Step-by-step explanation:

$to \: find = \\ position \: of \: θ \\ \\ so \: here \: \\ cosec \: θ - cot \: θ = 5 \\ \\ \: \: cosec \: θ = 5 + cot \: θ$

$we \: know \: that \\ 1 + cot {}^{2} \: θ = cosec {}^{2} \: θ \\ \\ = (cot \: θ + 5) {}^{2} \\ \\ 1 + cot {}^{2} \: θ= cot {}^{2} θ + 25 + 10.cot \: θ \\ \\ 1 - 25 = 10.cot \: θ \\ \\ - 24 = 10.cot \: θ \\ \\ cot \: θ = \frac{ - 24}{10} \\ \\ so \: as \: cot \: θ \: is \: negative \: \\ θ < 0 \\ \\ theta \: lies \: in \: quadrant \: 2$