Trigonometric Ratios and Identities
Multiple Angles
JEE Main 2017
Grade 11
Question:
If $5(\tan^2 x - \cos^2 x) = 2 \cos 2x + 9$, then the value of $\cos 4x$ is:
(1) $-\frac{7}{9}$
(2) $\frac{2}{9}$
(3) $\frac{1}{3}$
(4) $-\frac{1}{3}$
Step-by-Step Solution
Key Concept: Let $c = \cos 2x$. Write $\tan^2 x = (1 - c)/(1 + c)$ and $\cos^2 x = (1 + c)/2$. Substitute, simplify to a quadratic in $c$, solve, then use $\cos 4x = 2c^2 - 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)