Question

√[(1+tan²A)/(1+cot²A)]=tanA

Answer 1

Step-by-step explanation:

L.H.S. :

= root[(1 + tan^2 A)/(1 + cot^2 A)]

= root[sec^2 A / cosec^2 A]

= root[sin^2 A/cos^2 A]

=sin A/cos A

=tan A == R.H.S.

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Answer 2

Answer:

$\sqrt{ \frac{1 + tan^{2}x }{1 + cot ^{2} x} } = tanx \\ \\ \\ \\ = > \sqrt{ \frac{ \frac{cos^{2}x + {sin}^{2}x }{ {cos}^{2} x} }{ \frac{ {sin}^{2}x + {cos}^{2}x }{sin^{2}x } } } = \sqrt{ \frac{ {sin}^{2}x }{ {cos}^{2} x} } = \frac{sinx}{cosx} = tanx \: \: \: proved \\ \\ \\ \\ \\ hear \: \: let \: i \: \: a = x$

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