Trigonometric Ratios and Identities
Transformation Formulas
JEE Main 2019
Grade 11
Question:
The value of $\cos^2 10^\circ - \cos 10^\circ \cos 50^\circ + \cos^2 50^\circ$ is:
(1) $\frac{3}{4}$
(2) $\frac{3}{2}(1 + \cos 20^\circ)$
(3) $\frac{3}{4} + \cos 20^\circ$
(4) $\frac{3}{2}$
Step-by-Step Solution
Key Concept: Use $\cos A \cos B = \frac{1}{2}[\cos(A - B) + \cos(A + B)]$ and $\cos^2 \theta = (1 + \cos 2\theta)/2$. Group and simplify using $\cos 20^\circ + \cos 100^\circ = 2 \cos 60^\circ \cos 40^\circ = \cos 40^\circ$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)