Question

The equation $1+{\sin }^{2}ax=\cos x$ has a unique solution then a is

• A. rational
• B. irrational
• C. integer
• D. whole number

Answer 1

The correct option is B irrational

LHS $>1$
but RHS $<1$
solution exists only when LHS $=$ RHS $=1$
$\therefore \cos x=1$ and $\sin ax=0$
$ax=n\Pi$ and $x=2m\Pi$
clearly for unique solution, $a$ has to be irrational because of $a$ is rational then there will be many solutions