Question

The value of $\sqrt{\frac{1+cos\Theta}{1-cos\Theta} }$ is
(a)cot θ − cosec θ
(b)cosec θ + cot θ
(c)cosec²θ θ + cot²θ
(d)cosecθ+ cosec θ)²

Answer 1

Answer:

The value of √(1 + cosθ)/(1 - cosθ) is  cosec θ +  cotθ .

Among the given options option (b) cosec θ +  cotθ  is correct.  

Step-by-step explanation:

Given : √(1 + cosθ)/(1 - cosθ) = cosec θ +  cotθ

= √[(1 +  cosθ ) × (1+  cosθ )] / [(1- cosθ ) × (1 + cosθ )]

[By rationalising]

= √(1+  cosθ )²/(1 - cos²θ )

[By using an identity , (a + b) (a - b) = a² - b²]

= √[(1+  cosθ )²/(sin²θ )]

[By using  an identity, (1- cos²θ) = sin²θ]

= (1 +  cosθ )/(sinθ )

= 1/sinθ  + cosθ /sinθ  

= cosecθ  +  cotθ  

[By using , cosecθ = 1/sinθ & cotθ = cos θ/sinθ]

Hence, the value of √(1 + cosθ)/(1 - cosθ) is  cosec θ +  cotθ

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Answer 2

Answer:

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