Question

If cosec theta = x + 1/4x then the value of the cosec theta + cot theta is :-

1. 2x
2. -2x
3. 2/x
4. -1/2x


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Answer 1

Question:-

$\sf If \: cosec \theta = x + \frac{1}{4x} ,then \: the \: value \: of \: \\ \sf cosec \theta + cot \theta \: is \\ \sf(a) \: 2x. \\ \sf(b) \: - 2x. \\ \sf(c) \: \frac{2}{x} . \\ \sf(d) \: \frac{ - 1}{2x} .$

Solution:-

Let, cosecθ + cotθ = k ---> (1)

cosecθ – cotθ = 1/k ---> (2)

Adding (1) and (2), we get

$\sf 2cosecθ = k + \frac{1}{k}$

$\sf = > 2(x + \frac{1}{4k }) = k + \frac{1}{k}$

$\sf \: [ \because cosecθ = x + \frac{1}{4k} ]$

$\sf = > 2x + \frac{1}{2x} = k + \frac{1}{k}$

By comparing, we get k = 2k.

Answer:-

$\sf { \boxed{ \sf \large \pink{cosec \theta + cot \theta = 2x}}}$

Hope you have satisfied. ⚘