To solve the equation [tex]\( x^2 = 1 \)[/tex], we want to find the values of [tex]\( x \)[/tex] that satisfy this equation. Let's go through the solution step by step:
1. Rewrite the equation:
[tex]\[
x^2 = 1
\][/tex]
2. Isolate the variable:
To find [tex]\( x \)[/tex], we take the square root of both sides of the equation. Remember that taking the square root of a number can yield both a positive and a negative result.
[tex]\[
x = \pm \sqrt{1}
\][/tex]
3. Compute the square root:
The square root of 1 is 1. Therefore,
[tex]\[
x = \pm 1
\][/tex]
Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( x^2 = 1 \)[/tex] are [tex]\( 1 \)[/tex] and [tex]\( -1 \)[/tex].
Now, let's look at the multiple-choice options:
- Option a: [tex]\(\pm \sqrt{1}\)[/tex]: While this is mathematically correct in form, it is not the simplest representation of the solution.
- Option b: [tex]\(\pm 1\)[/tex]: This is the simplest and most accurate representation of the solutions.
- Option c: [tex]\(\sin^2 \theta + \cos^2 \theta\)[/tex]: This is a trigonometric identity that equals 1, but it doesn't directly provide the values of [tex]\( x \)[/tex].
- Option d: [tex]\(\cot^2 \theta - \operatorname{cosec}^2 \theta \)[/tex]: This is another trigonometric expression that does not relate directly to our equation.
The correct answer is:
[tex]\[ \text{b) } \pm 1 \][/tex]
