Question

Statement $1$: Number of solution of $n|\sin x|=m|\cos x|$, where $m,n\in Z$ in $(0,2\pi )$ is independent of $m$ and $n$.

Statement $2$: Multiplying trigonometric functions by constant changes only the range of the functions but period remains same.

• A. Both the statements are TRUE and Statement $2$ is the correct explanation of Statement $1$
• B. Both the statements are TRUE but Statement $2$ is NOT the correct explanation of Statement $1$
• C. Statement $1$ is TRUE and Statement $2$ is FALSE
• D. Statement $1$ is FALSE and Statement $2$ is TRUE

Answer 1

The correct option is D Statement $1$ is FALSE and Statement $2$ is TRUE

Case $1:$ $m,n>0$ and $m<n$

There are four solutions.


Case $2:$ $n>0,m<0$
Clearly, there is no solution.

So, we can conclude that number of solutions depend on the value of $m$ and $n$.

Statement $2$ is obviously true.