Number of common points for the curves y -sin -12 x -tan -11-2 x -2 and y -cos -12 x -5-1 is where - denotes greatest integerfunctionA- 1B- 0C- 3D- 4

The correct option is B 0As domain of first function is [ 1/2,0 ) ∪{1/2} and domain of 2^nd function [ 3, 2] there is no common point ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Number of com...

Question

Number of common points for the curves $y = s i n^{- 1} (2 x) + t a n^{- 1} (\frac{1}{[2 x]}) + 2$ and $y = c o s^{- 1} (2 x + 5) + 1$ is (where [.] denotes greatest integer function)

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Solution

As domain of first function is $[- \frac{1}{2}, 0) \cup {\frac{1}{2}}$ and domain of $2^{n d}$ function [-3, -2] there is no common point

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Number of common points for the curves y=sin−1(2x)+tan−1(1[2x])+2 and y=cos−1(2x+5)+1 is (where [.] denotes greatest integer function)

As domain of first function is [−12,0)∪{12} and domain of 2nd function [-3, -2] there is no common point

Number of common points for the curves $y = s i n^{- 1} (2 x) + t a n^{- 1} (\frac{1}{[2 x]}) + 2$ and $y = c o s^{- 1} (2 x + 5) + 1$ is (where [.] denotes greatest integer function)

As domain of first function is $[- \frac{1}{2}, 0) \cup {\frac{1}{2}}$ and domain of $2^{n d}$ function [-3, -2] there is no common point