Question

If sin theta=1/3 then find the value of(9 cot2 theta+9) is

Answer 1

Answer:

hope this will help you.

Answer 2

The value is $9\cot^2\theta+9=81$

Step-by-step explanation:

Given : $\sin\theta=\frac{1}{3}$

To find : The value of $9\cot^2\theta+9$ ?

Solution :

Write the expression as,

$9\cot^2\theta+9=9(\cot^2\theta+1)$

Using trigonometric property,  $\cot^2\theta+1=\csc^2\theta$

$9\cot^2\theta+9=9(\csc^2\theta)$

$9\cot^2\theta+9=9(\frac{1}{\sin^2\theta})$

Substitute the value,

$9\cot^2\theta+9=9(\frac{1}{(\frac{1}{3})^2})$

$9\cot^2\theta+9=9(\frac{1}{\frac{1}{9}})$

$9\cot^2\theta+9=9(9)$

$9\cot^2\theta+9=81$

Therefore, the value is $9\cot^2\theta+9=81$

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