Question

You are given a matrix nxm filled with integers. There is a robot which has to travel from the cell (1,1) to cell (n,m) and the robot can move only one cell to the right or downwards. The robot requires strength to travel from one cell to another. He can only move forward if his strength is positive. When he moves to a cell , the cell value is added to his strength(value can be negative or positive). Calculate the minimum strength you have to give to the robot initially so that he can make it to the last cell.

Answer 1

Answer:

Step-by-step explanation:

$\huge \underline \mathfrak {Solution:-}$

$\begin{lgathered}\frac{ 1}{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } = k \\ \\ \frac{(1 + \cos(x) )}{ \sin(x) } = k \\ \\ \frac{2 \cos {}^{2} ( \frac{x}{2} ) }{2 \sin(x ) \cos(x) } = k \\ \\ \frac{ \cos( \frac{x}{2} ) }{ \sin( \frac{x}{2} ) } = k \: \: \: \: \: \: \: \: ......(1)\end{lgathered}$

$\begin{lgathered}\frac{ {k}^{2} - 1}{ {k}^{2} + 1} \\ \\ = \frac{ \frac{ \cos {}^{2} ( \frac{x}{2} ) }{ \sin {}^{2} ( \frac{x}{2} ) } - 1 }{ \frac{ \cos {}^{2} ( \frac{x}{2} ) }{ \sin {}^{2} ( \frac{x}{2} ) } + 1 } \\ \\ = \frac{\cos {}^{2} ( \frac{x}{2} ) -\sin {}^{2} ( \frac{x}{2} ) }{\cos {}^{2} ( \frac{x}{2} ) + \sin {}^{2} ( \frac{x}{2} )} \\ \\ = \frac{ \cos(x) }{1} \\ \\ = \cos(x)\end{lgathered}$