3 c o s − 1 x − π x − π 2 = 0 has : Options: A . &nbspOne solution B . &nbspInfinite solutions C . &nbspNo solution D . &nbspNone of these

3cos−1x−πx−π2=0 has :

Question

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

has :

Options:

A . One solution

B . Infinite solutions

C . No solution

D . None of these

Answer: Option A
:
A

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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