^ 1( 1)=π ^ 1(1) (∵^ 1( x)=π ^ 1(x), x∈ℝ) ⇒ nbsp;^ 1( 1)=π π4=3π4 ...

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Differentiation of Inverse Trigonometric Functions

The value of ...

Question

The value of ${cot}^{- 1} (- 1)$ is

\frac{5 π}{4}

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\frac{3 π}{4}

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\frac{- π}{4}

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\frac{π}{4}

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Solution

The correct option is B $\frac{3 π}{4}$
${cot}^{- 1} (- 1) = π - {cot}^{- 1} (1) (∵ {cot}^{- 1} (- x) = π - {cot}^{- 1} (x), x \in R) \Rightarrow {cot}^{- 1} (- 1) = π - \frac{π}{4} = \frac{3 π}{4}$

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