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From$\lambda cosx> -2$

how they have derived the value of $\lambda$

Koolman
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  • I'm seeing some kind of Indian writing that I don't understand. This question has been nominated to be closed, and the Indian writing does not help. – Robert Soupe Mar 26 '17 at 20:41
  • @RobertSoupe It has both language Hindi and english . and both means the same . – Koolman Mar 27 '17 at 09:51
  • I would advise you in the future to not include Hindi in your questions (or answers) unless it is absolutely necessary. – Robert Soupe Mar 27 '17 at 17:02

1 Answers1

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For all $x \in \mathbb R$, we have $$- 1\leq \cos x \leq 1$$ so if $\lambda \geq 0$ one has $$ - \lambda \leq \lambda\cos x \leq \lambda$$ So if one wants $ \lambda\cos x >-2$ one must have $-\lambda \geq -2$ that is to say $\lambda \leq 2$. Since $\lambda$ is an integer $\lambda = 0,1,2$.

Now if $\lambda < 0$ one has $$ - \lambda \geq \lambda\cos x \geq \lambda$$ so $\lambda \geq -2$ that implies $\lambda = -1,-2$ (using the same argument).

Héhéhé
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