Trigonometric Ratios and Identities
Inverse Trigonometry applied to Trig
JEE Main 2024
Grade 11
Question:
Let $\tan A = \frac{1}{\sqrt{x(x^2 + x + 1)}}$, $\tan B = \frac{\sqrt{x}}{\sqrt{x^2 + x + 1}}$, and $\tan C = \sqrt{\frac{x^2 + x + 1}{x^3}}$, where $A, B, C \in \left(0, \frac{\pi}{2}\right)$. Find $A + B + C$ in degrees.
Step-by-Step Solution
Key Concept: Compute $\tan(A + B)$ using the addition formula and simplify. Show $\tan(A + B) = \tan C$, which (with all angles acute and summing $< 270^\circ$) gives $A + B + C = 180^\circ$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 180