If k ≤ sin − 1 x + cos − 1 x + tan − 1 x ≤ K , then −

sin − 1 x + cos − 1 x + tan − 1 x = 2 π + tan − 1 x Since domain of the function x ∈ [ − 1 , 1 ] ∴ − 4 π ≤ tan − 1 x ≤ 4 π Hence, k = 4 π and K = 4 3 π

Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionGeneral ( General, Domain, Range & Graph)Hard2 minPYQ_2012

MathematicsHardsingle choice

If $k \leq sin^{- 1} x + cos^{- 1} x + tan^{- 1} x \leq K,$ then $-$

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Answer:

Solution:

$sin^{- 1} x + cos^{- 1} x + tan^{- 1} x = \frac{π}{2} + tan^{- 1} x$ Since domain of the function $x \in [- 1, 1]$ $∴ - \frac{π}{4} \leq tan^{- 1} x \leq \frac{π}{4}$ Hence, $k = \frac{π}{4}$ and $K = \frac{3 π}{4}$

Stream:BITSATSubject:MathematicsTopic:Inverse Trigonometric FunctionSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: PYQ_2012

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