Questions: Simplify to a single trig function with no denominator. 9 sin^2 x - 9

Solution Steps

To simplify the given expression \( 9 \sin^2 x - 9 \) to a single trigonometric function with no denominator, we can factor out the common term and use a trigonometric identity.

1. Factor out the common term \( 9 \).
2. Use the Pythagorean identity \( \sin^2 x + \cos^2 x = 1 \) to simplify the expression.

Given the expression: \[ 9 \sin^2 x - 9 \] we can factor out the common term \( 9 \): \[ 9 (\sin^2 x - 1) \]

We know from the Pythagorean identity that: \[ \sin^2 x + \cos^2 x = 1 \] Rearranging this identity, we get: \[ \sin^2 x - 1 = -\cos^2 x \] Substituting this into our expression, we have: \[ 9 (\sin^2 x - 1) = 9 (-\cos^2 x) \]

Simplifying the expression, we get: \[ 9 (-\cos^2 x) = -9 \cos^2 x \]

Final Answer