Find common denominator: \(\frac{\sin^2 \theta + (1 + \cos \theta)^2}{\sin \theta(1 + \cos \theta)}\). Expand numerator: \(\sin^2 \theta + 1 + 2\cos \theta + \cos^2 \theta = (\sin^2 \theta + \cos^2 \theta) + 1 + 2\cos \theta = 1 + 1 + 2\cos \theta = 2 + 2\cos \theta = 2(1 + \cos \theta)\). So expression becomes \(\frac{2(1 + \cos \theta)}{\sin \theta(1 + \cos \theta)} = \frac{2}{\sin \theta} = 2\csc \theta\).

Break down complex topics into smaller, manageable chunks for easier recall.

Zambia

• Joseph Soko – 101 pts

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