First slide

Trigonometric equations

Question

Number of integral values of ‘a’ satisfying the equation ${[\cos x]}^{2} + \cos x = 2 a$ is (where [ ] denotes G.I.F)

Moderate

A

1
B

2
C

3
D

4

Solution

$2 a = {[\cos x]}^{2} + \cos x$ , here $a \in I$
$\Rightarrow \cos x \in I$
$\Rightarrow \cos x = - 1 o r 0 o r 1$
$\Rightarrow 2 a = \cos^{2} x + \cos x = 0 o r 2$
$\Rightarrow$ a= 0 or 1

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