Question

cosec theta equals to a + 1 / 4 a, then cosec theta + cot theta equals to​

Answer 1

answer of your question

Answer 2

given

$cosec \theta = a + \frac{1}{4a}$

we know

${cot}^{2} \theta = {cosec}^{2} \theta - 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: = ( {a + \frac{1}{4a} })^{2} - 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {a}^{2} + \frac{1}{16 {a}^{2} } + \frac{1}{2} - 1 \\ \\ = {a}^{2} + \frac{1}{16 {a}^{2} } - \frac{1}{2}$

$\therefore \: \: cot \theta = ± \sqrt{( {a - \frac{1}{4a} })^{2} } \\ \\ = ±(a - \frac{1}{4a} )$

Now

$cosec \theta + cot \theta \\ \\ = a + \frac{1}{4a} + a - \frac{1}{4a} \\ \\ = 2a$

and

$cot \theta + cosec \theta \\ \\ = - a + \frac{1}{4a} + a + \frac{1}{4a} \\ \\ = \frac{1}{2a}$