Questions: (1-sin^2(theta)-1-sin^2(theta))/(sin^4(theta))

Solution Steps

To simplify the given expression, we can use trigonometric identities. The identity \(1 - \sin^2 \theta = \cos^2 \theta\) can be applied to simplify the numerator. After simplifying, we can divide the terms in the numerator by the denominator.

We start with the expression

\[ \frac{1 - \sin^2 \theta - 1 - \sin^2 \theta}{\sin^4 \theta}. \]

Using the identity \(1 - \sin^2 \theta = \cos^2 \theta\), we can rewrite the numerator:

\[ 1 - \sin^2 \theta - 1 - \sin^2 \theta = -2\sin^2 \theta. \]

Thus, the expression simplifies to

\[ \frac{-2\sin^2 \theta}{\sin^4 \theta}. \]

Next, we can simplify the fraction:

\[ \frac{-2\sin^2 \theta}{\sin^4 \theta} = -2 \cdot \frac{1}{\sin^2 \theta} = -\frac{2}{\sin^2 \theta}. \]

Final Answer