Question

If $sin\Theta=\frac{1}{3}$, then find the value of 2cot²θ θ + 2

Answer 1

Answer:

The value of 2cot²θ + 2 is 18.

Step-by-step explanation:

Given : sinθ = ⅓

By using  , cosec θ = 1/sinθ

cosec θ = 1/(⅓) = 1 × (3/1) = 3

By using the identity , cosec² θ -  cot²θ = 1

(3)² - cot²θ = 1

9 - cot²θ = 1

cot²θ = 9 - 1  

cot²θ = 8

We have to find the value of, 2cot²θ + 2 :  

2cot²θ + 2

= 2 (8)+ 2  

= 16 + 2

= 18

Hence, the value of 2cot²θ + 2 is 18.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

$Value \:of \: 2cot^{2}\theta+2=18$

Step-by-step explanation:

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

$\implies cosec\theta \\= \frac{1}{sin\theta}\\=\frac{1}{\frac{1}{3}}\\=3\:---(3)$

$Now, \\Value \:of \: 2cot^{2}\theta+2\\=2(cot^{2}\theta+1)\\=2Cosec^{2}\theta$

/* By Trigonometric identity:

1+cot²A = cosec²A */

$=2 \times 3^{2}\:[From \:(2)]$

$= 2 \times 9\\=18$

Therefore,

$Value \:of \: 2cot^{2}\theta+2=18$

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