Question

verify tan90⁰=2tan45⁰/1-tan²45⁰​

Answer 1

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You must know that,

$\boxed{\mathfrak{ tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}}}$

tan 90 can be written as tan(45 + 45)

Using the above mentioned formula,

$tan(45+45)=\frac{tan45+tan45}{1-tan45tan45}$

$tan90=\frac{2tan 45}{1-tan^{2}45 }$

Hence proved!