Electric current $(I)$ is measured by galvanometer, the current being proportional to the tangent of the angle ( $\theta$ ) of deflection. If the deflection is read as $45^{\circ}$ and an error of $1 \%$ is made in reading it, the percentage error in the current is

If the equation of a tangent drawn to the curve $y=\cos (x+y),-1 \leq x \leq 1+\pi$ is $x+2 y=k$, then $k=$

$f: R \rightarrow R$ is a function defined by $f(x)=\frac{1}{e^x+2 e^{-x}}$

Assertion (A) : $f(c)=\frac{1}{3}$ for some values of $c \in R$

Reason (R) : $0 < f(x) \leq \frac{1}{2 \sqrt{2}}$ for all $x \in R$

Then, which of the following options is correct?