Question
The Function $\text{f}(\text{x})=\frac{\lambda+\sin\text{x}+2\cos\text{x}}{\sin\text{x}+\cos\text{x}}$ is increasing, if:
- $\lambda<1$
- $\lambda>1$
- $\lambda<2$
- $\lambda>2$
Solution:
$\text{f}(\text{x})=\frac{\lambda+\sin\text{x}+2\cos\text{x}}{\sin\text{x}+\cos\text{x}}$
$\Rightarrow\text{f}(\text{x})=(\lambda-2)\sin^2\text{x}+(\lambda-2)\cos^2\text{x}>0$
Using identity $\Rightarrow\lambda-2>0$
$\Rightarrow\lambda>2$
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