Question

simplify (sin^2(x)+2sin(x)+1)/(sin^2(x)+sin(x))

Answer 1

Answer on Question #82801 – Math – Trigonometry

Question

simplify $(\sin^2(x) + 2\sin(x) + 1) / (\sin^2(x) + \sin(x))$

Solution

$$\frac{\sin^2 x + 2 \sin x + 1}{\sin^2 x + \sin x} = \frac{(1 + \sin x)^2}{\sin x (1 + \sin x)} = \frac{1 + \sin x}{\sin x} = \frac{1}{\sin x} + 1 = \text{cosecx} + 1.$$

Answer: $\frac{\sin^2 x + 2 \sin x + 1}{\sin^2 x + \sin x} = \text{cosecx} + 1.$

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