Quadratic Equations
Transcendental Equation — Number of Solutions
nta_pyq_2024_jan
Grade 11
Question:
The number of solutions of the equation $e^{\sin x}-2e^{-\sin x}=2$ is
Step-by-Step Solution
Key Concept: Let $t=e^{\sin x}>0$. Equation: $t-2/t=2\Rightarrow t^2-2t-2=0\Rightarrow t=1\pm\sqrt{3}$. Since $t>0$: $t=1+\sqrt{3}\approx2.73$. Then $\sin x=\ln(1+\sqrt3)>1$, which is impossible.
$t=1+\sqrt3\Rightarrow\sin x=\ln(1+\sqrt3)>1$: impossible. No solutions.
Correct Answer: 4