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Question
If tanx = `b/a`, then find the value of `sqrt((a + b)/(a - b)) + sqrt((a - b)/(a + b))`
Solution
Given that: tan x = `b/a`
`sqrt((a + b)/(a - b)) + sqrt((a - b)/(a + b)) = sqrt(a + b)/sqrt(a - b) + sqrt(a - b)/sqrt(a + b)`
= `(a + b + a - b)/sqrt((a - b)(a + b))`
= `(2a)/sqrt(a^2 - b^2)`
= `(2a)/(asqrt(1 - b^2/a^2))`
= `2/sqrt(1 - tan^2x)`
= `2/sqrt(1 - (sin^2x)/(cos^2x))`
= `2/(sqrt(cos^2x - sin^2x)/cosx)`
= `(2cosx)/sqrt(cos2x)` ......`[because cos^2x - sin^2x = cos2x]`
Hence, `sqrt((a + b)/(a - b)) + sqrt((a - b)/(a + b)) = (2cosx)/sqrt(cos2x)`.
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