To simplify the expression cot^2(x) + sc(x) - 1, let's break it down step-by-step:
1. Start with cot^2(x): This is the square of the cotangent function. Remember that cot(x) is equal to 1/tan(x). So cot^2(x) can be rewritten as (1/ tan(x))^2.
2. Simplify cot^2(x): Squaring a fraction means multiplying the numerator and denominator by itself. So, (1/tan(x)^2 becomes (1^2)/(tan(x)^2, which simplifies to 1/(tan(x)\^2.
3. Move on to sc(x): The cosecant function is the reciprocal of the sine function, so sc(x) is equal to 1/sin(x).
4. Combine the terms: Now, we have 1/(tan(x) ^2 + 1/sin(X) - 1.
5. Common denominator: To combine the fractions, we need a common denominator. The common denominator here is (sin(x))^2. So, we need to multiply the first fraction by (sin(x)^2/(sin(×^2 and the second fraction by (tan(×^2/(tan(x)^2.
6. Rewrite the expression with a common denominator: After multiplying the fractions by their respective forms of 1, we have (1/(tan(x))^2)*(sin(x)^2/ (sin(x))^2 + (1/sin(x))*(tan(x))^2/(tan(x))^2 - 1*(sin(x) ^2/(sin(x)^2.
7. Simplify the fractions: Now we have (sin(x))^2/(tan(x))^2*(sin(x))^2+(tan(x))^2/(sin(x))^2*(tan(x))^2-(sin(x)^2/(sin(x))^2.
8. Simplify the numerators and denominators: In the first fraction, (sin(x)2 cancels out with (sin(x)^2, leaving us with just (sin(x))^2 in the numerator.
In the second fraction, (tan(×^2 cancels out with (sin(x)^2, leaving us with just (tan(x))^2 in the numerator. And in the third fraction, (sin(x)½^2 cancels out with (sin(x)) 2, leaving us with 1 in the numerator.
9. Combine the terms: Now we have (sin(x)\^2 + (tan(x)^2 - 1.
So, the simplified expression is (sin(x))^2 + (tan(x))^2 - 1.