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Prove That: √ Sec θ − 1 Sec θ + 1 + √ Sec θ + 1 Sec θ − 1 = 2 Cos E C θ - Mathematics

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Sum

Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`

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Solution

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = sqrt(sectheta - 1)/sqrt(sectheta + 1) + sqrt(sectheta + 1)/sqrt(sectheta - 1)`

= `(sqrt(sectheta - 1)sqrt(sectheta - 1) + sqrt(sectheta + 1)sqrt(sectheta + 1))/(sqrt(sectheta + 1)sqrt(sectheta - 1))`

= `((sqrt(sectheta - 1))^2 + (sqrt(sectheta + 1))^2)/sqrt((sectheta - 1)(sectheta + 1))`

= `(sectheta - 1 + sectheta + 1)/sqrt(sec^2theta - 1)`

= `(2sectheta)/sqrt(tan^2theta)`

= `(2sectheta)/tantheta` 

= `(2 1/costheta)/(sintheta/costheta)`

= `2 1/sintheta`

= `2 cosectheta`

Concept: Trigonometric Identities
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