Use the compound angle formulae to rewrite: \( 1.1 \cos (\theta+2 \beta) \) \( 1.2 \cos (3 x-y) \) \( 1.3 \sin (3 \theta+2 \beta) \) \( 1.4 \sin (x-4 y) \)

Sure! Here’s how you can rewrite those expressions using the compound angle formulae: For \( 1.1 \cos (\theta + 2\beta) \): \[ \cos(\theta + 2\beta) = \cos \theta \cos (2\beta) - \sin \theta \sin (2\beta) \] So, \[ 1.1 \cos (\theta + 2 \beta) = \cos \theta \cos (2\beta) - \sin \theta \sin (2\beta) \] For \( 1.2 \cos (3x - y) \): \[ \cos(3x - y) = \cos(3x) \cos(y) + \sin(3x) \sin(y) \] Thus, \[ 1.2 \cos (3 x - y) = \cos(3x) \cos(y) + \sin(3x) \sin(y) \] For \( 1.3 \sin (3\theta + 2\beta) \): \[ \sin(3\theta + 2\beta) = \sin(3\theta) \cos(2\beta) + \cos(3\theta) \sin(2\beta) \] Therefore, \[ 1.3 \sin (3 \theta + 2 \beta) = \sin(3\theta) \cos(2\beta) + \cos(3\theta) \sin(2\beta) \] For \( 1.4 \sin(x - 4y) \): \[ \sin(x - 4y) = \sin(x) \cos(4y) - \cos(x) \sin(4y) \] So, \[ 1.4 \sin(x - 4 y) = \sin(x) \cos(4y) - \cos(x) \sin(4y) \]