Geometry
# Sum and Difference Trigonometric Formulas

Given that \(\sin^2 \theta = \frac{1}{3}\), what is the value of \(72 \cos(2 \theta)\)?

The double angle identity states that

\[ \cos (2 \theta) = N \cos^2 \theta - M, \]

where \(N\) and \(M\) are real numbers. What is the value of \( N + M \)?

The double angle identity states that

\[ \sin ( 2 \theta ) = N \sin \theta \cos \theta + M, \]

where \(N\) and \(M\) are real numbers. What is the value of \(N + M \)?