MCQ
The function $\sin x - \cos x$ is increasing in the interval
- A$\left[ {{{3\pi } \over 4},{{7\pi } \over 4}} \right]$
- ✓$\left[ {0,{{3\pi } \over 4}} \right)$
- C$\left[ {{\pi \over 4},{{3\pi } \over 4}} \right]$
- DNone of these
Now $f(x)$ is increasing function of $x$ , if
$f'(x) = \cos x + \sin x > 0$ or $\sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right) > 0$
==>$0 \le x < \frac{{3\pi }}{4}i.e.\,\,\,f'(x) > 0$ in $\left[ {0,\frac{{3\pi }}{4}} \right)$.
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$(1)$ $y=\log _0\left(\frac{1+\sqrt{1-x^2}}{x}\right)-\sqrt{1-x^2}$
$(2)$ $x y^{\prime}-\sqrt{1-x^2}=0$
$(3)$ $y=-\log _0\left(\frac{1+\sqrt{1-x^2}}{x}\right)+\sqrt{1-x^2}$
$(4)$ $x y^{\prime}+\sqrt{1-x^2}=0$
If
$\begin{bmatrix}2\text{x}+\text{y}&4\text{x}\\5\text{x}-7&4\text{x}\end{bmatrix}=\begin{bmatrix}7&7\text{y}-13\\\text{y}&\text{x}+6\end{bmatrix},$ then the value of x + y is: