# If tan x = b/a... Then find whole under root (a+b)/a-b) + whole under rt (a- b)/(a+b)...

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by meherdeep

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by meherdeep

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or, tanx+1 = b/a+1

or, tanx+1 = (b+a)/a

or, a(tanx) = a+b -------------(1)

or, tanx-1 = b/a-1

or, tanx-1 = (b-a)/a

or, a(tanx-1) = b-a

or, a(1-tanx) = a-b-------------(2)

now,under root[(a+b)/(a-b)] + under root[(a-b)/(a+b)]

put the value of a+b & a-b from (1) & (2)

or, under root[a(1+tanx)/a(1-tanx)] + under root[a(1-tanx)/a(1+tanx)]

or, under root[(1+tanx)/(1-tanx)] + under root[(1-tanx)/(1+tanx)]

when we rationalize the terms

or, under root[(1+tanx)^2/(1^2-tan^2x)] + under root[(1-tanx)^2/(1^2-tan^2x)]

or, (1+tanx)/root(1-tan^2x) + (1-tanx)/root(1-tan^2x)

or, (1+tanx+1-tanx)/root(1-tan^2x)

or, 2/root(1-tan^2x)