Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Easy2 minQB

MathematicsEasysingle choice

A value of $x$ satisfying the equation $\sin [\cot^{- 1} (1 + x)] = \cos [\tan^{- 1} x],$ is:

Answer:

Solution:

$sin (cot^{- 1} (1 + x)) = cos (tan^{- 1} x)$

Let $cot λ = 1 + x$ .

$tan β = x$

$\Rightarrow sin λ = cos β$

$\Rightarrow \frac{1}{x ^{2} + 2 x + 2} = \frac{1}{1 + x ^{2}}$

$\Rightarrow x^{2} + 2 x + 2 = x^{2} + 1$

$\Rightarrow x = - 1/2$ $\Rightarrow x = - 1 / 2$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: QB

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