Trigonometry & Inverse Trigonometry
Range of a trigonometric expression
nta_pyq_2023_jan
Grade 11
Question:
The set of all values of $\lambda$ for which the equation $\cos^2 2x - 2\sin^4 x - 2\cos^2 x = \lambda$ has a real solution $x$ is
$[-2, -1]$
$\left[-2, -\frac{3}{2}\right]$
$\left[-1, -\frac{1}{2}\right]$
$\left[-\frac{3}{2}, -1\right]$
Step-by-Step Solution
Key Concept: Express $\lambda$ entirely in terms of $\cos^2 x$, then find the range of the resulting expression.
$\lambda \in [-3/2, -1]$. Answer: (4)
Correct Answer: $\left[-\frac{3}{2}, -1\right]$