Question

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If cot theta + cosec theta = l, then find the value of tan theta in terms of l.

Answer 1

Answer:

tan theta = 1/ ( I- cosec theta)

Answer 2

Answer:

$\frac{2l}{l - 1}$

Step-by-step explanation:

Given: cot θ + cosecθ = l

To find: Tanθ in terms of l

Solution:

We know that,  $cosec^{2}$ θ = $1 + cot^{2}$ θ                    .................(1)

putting the value of equation (1) in given equation,

⇒ √($1 + cot^2$θ) + cotθ = l

⇒ √($1 + cot^2$θ) = l - cotθ

squaring both sides,

⇒ 1 + $cot^2$ θ = (l - cotθ)²

⇒ 1 + $cot^2$ θ = l + $cot^2$ θ - 2lcotθ

⇒ 1 - l =  - 2lcotθ

⇒ cotθ = $\frac{l - 1}{2l}$

⇒ tanθ = $\frac{2l}{l - 1}$

∴ $tan$θ$= \frac{2l}{l - 1}$

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