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Question
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
Options
cot θ − cosec θ
cosec θ + cot θ
cosec2 θ + cot2 θ
(cot θ + cosec θ)2
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Solution
The given expression is `sqrt ((1+cosθ)/(1-cos θ))`
Multiplying both the numerator and denominator under the root by` (1+cosθ )`, we have
`sqrt (((1+cosθ)(1+cosθ))/((1+cosθ)(1-cos θ)))`
`=sqrt ((1+cosθ)^2/ ((1-cos^2 θ))`
`=sqrt((1+cos θ)^2/sin^2θ`
`=(1+cos θ)/(sinθ)`
= `1/sinθ+cosθ/sinθ`
= `cosecθ+cotθ`
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