Question

If 3cot θ= 1, then the value of cosec θ is :

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:cosec\:\theta\:=\:\dfrac{\sqrt{10}}{3}\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:3\:\cot\:\theta\:=\:1}$

We have to find the value of $\displaystyle{\sf\:cosec\:\theta}$

Now,

$\displaystyle{\sf\:3\:\cot\:\theta\:=\:1}$

$\displaystyle{\implies\sf\:\cot\:\theta\:=\:\dfrac{1}{3}}$

Now, we know that,

$\displaystyle{\pink{\sf\:cosec^2\:\theta\:=\:1\:+\:\cot^2\:\theta}}$

$\displaystyle{\implies\sf\:cosec^2\:\theta\:=\:1\:+\:\left(\:\dfrac{1}{3}\:\right)^2}$

$\displaystyle{\implies\sf\:cosec^2\:\theta\:=\:1\:+\:\dfrac{1}{9}}$

$\displaystyle{\implies\sf\:cosec^2\:\theta\:=\:\dfrac{9\:+\:1}{9}}$

$\displaystyle{\implies\sf\:cosec^2\:\theta\:=\:\dfrac{10}{9}}$

$\displaystyle{\implies\sf\:cosec\:\theta\:=\:\sqrt{\dfrac{10}{9}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:cosec\:\theta\:=\:\dfrac{\sqrt{10}}{3}\:}}}}$

Answer 2

Question

If 3cot θ= 1, then the value of cosec θ is :

To find;

The value of cosec ∅ = ?

Answer

3cos ∅ = 1

cos ∅ = ⅓

cos²∅= ⅑

1-sin²∅= 1-⅑

sin ∅ = 1-⅑

sin ∅ = √8/9

sin∅ = 2√2/3

cosec∅ = 1/sin∅ = 3/2√2

$\huge{ \boxed{ \green{ \tt \: answer : \: = \frac{3}{ 2 \sqrt{2} } }}}$