Number of common points for the curves y-sin-12x-tan-1 1-2x- -2 and y-cos-12x-5-1 is where - denotes greatest integer function

As 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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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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y = s i n^{- 1} (2 x) + t a n^{- 1} (\frac{1}{[2 x]}) + 2

y = c o s^{- 1} (2 x + 5) + 1

y = [| s i n x | + | c o s x |] a n d x^{2} + y^{2} = 5

[y + [y]] = 2 cos x

y = \frac{1}{3} [sin x + [sin x + [sin x]]]

The angle of intersection of curves. y = [|sin x| + |cos x|] and $x^{2} + y^{2} = 5$ where [.] denotes greatest integral function is

\frac{sin x}{sin y} = \frac{1}{2}, \frac{cos x}{cos y} = \frac{3}{2}

x, y \in (0, \frac{π}{2})

tan (x + y)

k

[k] =

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