tan^ 1(2^x+11 (2^x)^2) = tan^ 1(2.2^x1 (2^x)^2) = tan^ 1(tan(2.2^x)) = 2^x+1 #160; ...

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Byju's Answer

Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

Solve Tan-1 ...

Question

Solve
$T a n^{- 1} (\frac{2^{x + 1}}{1 - 4^{x}})$

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Solution

$t a n^{- 1} (\frac{2^{x + 1}}{1 - (2^{x})^{2}}) = t a n^{- 1} (\frac{{2.2}^{x}}{1 - (2^{x})^{2}})$
$= t a n^{- 1} (t a n ({2.2}^{x}))$
$= 2^{x + 1} ★$

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SolveTan−1(2x+11−4x)

tan−1(2x+11−(2x)2)=tan−1(2.2x1−(2x)2)=tan−1(tan(2.2x))=2x+1★

Solve
$T a n^{- 1} (\frac{2^{x + 1}}{1 - 4^{x}})$

$t a n^{- 1} (\frac{2^{x + 1}}{1 - (2^{x})^{2}}) = t a n^{- 1} (\frac{{2.2}^{x}}{1 - (2^{x})^{2}})$
$= t a n^{- 1} (t a n ({2.2}^{x}))$
$= 2^{x + 1} ★$