Identify Trigonometric Identity: Step Title: Identify the Trigonometric Identity Concise Step Description: Recognize that the denominator is a quadratic in terms of sin(x) and can be factored. Calculation: No calculations in this step.Factor Denominator: Step Title: Factor the Denominator Concise Step Description: Factor the quadratic expression in the denominator. Calculation: We need to find two numbers that multiply to -2 (the constant term) and add to 1 (the coefficient of the middle term, sin(x)). The numbers that satisfy these conditions are 2 and -1. Factored form of the denominator: (sin(x) + 2)(sin(x) - 1).Simplify Expression: Step Title: Simplify the Expression Concise Step Description: Write the simplified form of the expression with the factored denominator. Calculation: The expression becomes cos(x) / ((sin(x) + 2)(sin(x) - 1)).

Algebra 2

Factor polynomials

Full solution

\frac{cosx}{(sin^2x+sinx-2)}

Identify Trigonometric Identity: Step Title: Identify the Trigonometric Identity $\newline$ Concise Step Description: Recognize that the denominator is a quadratic in terms of $\sin(x)$ and can be factored. $\newline$ Calculation: No calculations in this step.
Factor Denominator: Step Title: Factor the Denominator $\newline$ Concise Step Description: Factor the quadratic expression in the denominator. $\newline$ Calculation: We need to find two numbers that multiply to $-2$ (the constant term) and add to $1$ (the coefficient of the middle term, $\sin(x)$ ). The numbers that satisfy these conditions are $2$ and $-1$ . $\newline$ Factored form of the denominator: $(\sin(x) + 2)(\sin(x) - 1)$ .
Simplify Expression: Step Title: Simplify the Expression $\newline$ Concise Step Description: Write the simplified form of the expression with the factored denominator. $\newline$ Calculation: The expression becomes $\frac{\cos(x)}{(\sin(x) + 2)(\sin(x) - 1)}$ .