Final Answer:
The simplified expression for (sin²x-1)/(sinx+1) is (sinx-1).
Step-by-step explanation:
To simplify the given expression (sin²x-1)/(sinx+1), we can factor the numerator and denominator. The numerator can be factored as a difference of squares, yielding (sinx+1)(sinx-1). The denominator remains unchanged. Now, we can cancel out the common factor of (sinx-1) from both the numerator and denominator, leaving us with the simplified expression of (sinx-1).
In mathematical terms, the steps involve factoring the numerator as (sinx+1)(sinx-1) and leaving the denominator unchanged. Then, canceling out the common factor of (sinx-1) from both the numerator and denominator. The final simplified expression is (sinx-1). This simplification is valid as long as sinx is not equal to -1, which would make the original denominator equal to zero.
In conclusion, the expression (sin²x-1)/(sinx+1) simplifies to (sinx-1), with the understanding that the simplification is valid for all values of x where sinx is not equal to -1. This process of factoring and canceling common factors helps to express the given expression in a simpler and more manageable form.