3cos-1 x - - x - -2 - 0 has -

3cos^ 1 x π x + π/2 Clearly graphs of y = 3cos^ 1 x and y = π x + π/2 in the domain of cos^ 1 x i.e., in [ 1, 1] intersect only once, therefore there is onl ...

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Standard XII

Mathematics

Graphs of Basic Inverse Trigonometric Functions

3cos-1 x - π ...

Question

$3 c o s^{- 1} x - π x - \frac{π}{2} = 0$ has :

One solution

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Infinite solutions

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No solution

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None of these

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Solution

The correct option is A One solution

$3 c o s^{- 1} x - π x + \frac{π}{2}$
Clearly graphs of $y = 3 c o s^{- 1} x$ and $y = π x + \frac{π}{2}$ in the domain of $c o s^{- 1} x$ i.e., in [-1, 1] intersect only once, therefore there is only one solution of the given equation.

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Similar questions

Q. The equation

3 c o s^{- 1} x - π x - \frac{π}{2} = 0

has

3 c o s^{- 1} x - π x - \frac{π}{2} = 0

has :

Q. Match the column

	List I		List II
A.	Range of $f (x) = {sin}^{- 1} x + {cos}^{- 1} x + {cot}^{- 1} x$ is	1.	$[0, \frac{π}{2}) \cup (\frac{π}{2}, π]$
B.	Range of $f (x) = cot - 1 x + {tan}^{- 1} x + c o s e c^{- 1} x$ is	2.	$[\frac{π}{2}, \frac{3 π}{2}]$
C.	Range of $f (x) = {cot}^{- 1} x + {tan}^{- 1} x + {cos}^{- 1} x$ is	3.	${0, π}$
D.	Range of $f (x) = {sec}^{- 1} x + c o s e c^{- 1} x + {sin}^{- 1} x$ is	4.	$(\frac{π}{2}, \frac{3 π}{2})$

Q. The remainder obtained on dividing the polynomial

p (x) = {(πx)}^{4} + {2 (πx)}^{3} - {2 (πx)}^{2} + 6 (πx) + 4

by another polynomial

x + π^{- 1}

is .

Q. Prove that :

3 c o s^{- 1} x = c o s^{- 1} (4 x^{3} - 3 x)

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3cos−1x−πx−π2=0 has :

The correct option is A One solution 3cos−1x−πx+π2 Clearly graphs of y=3cos−1x and y=πx+π2 in the domain of cos−1x i.e., in [-1, 1] intersect only once, therefore there is only one solution of the given equation.

$3 c o s^{- 1} x - π x - \frac{π}{2} = 0$ has :

The correct option is A One solution

$3 c o s^{- 1} x - π x + \frac{π}{2}$
Clearly graphs of $y = 3 c o s^{- 1} x$ and $y = π x + \frac{π}{2}$ in the domain of $c o s^{- 1} x$ i.e., in [-1, 1] intersect only once, therefore there is only one solution of the given equation.