3 cos -1 x- x-2-0 hasA- One solutionB- Infinite solutionsC- No solutionD- None of these

The correct option is A One solution 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] inters ...

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Standard XII

Mathematics

Graphs of Basic Inverse Trigonometric Functions

3 cos -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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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.