Absolutely, let's dive into solving the equation step-by-step:
Given the equation:
[tex]\[
\sin^2 \theta + \cos^2 \theta = x - 25
\][/tex]
1. Understand and apply the trigonometric identity:
Recall one of the fundamental trigonometric identities:
[tex]\[
\sin^2 \theta + \cos^2 \theta = 1
\][/tex]
2. Substitute the identity into the equation:
Replace [tex]\(\sin^2 \theta + \cos^2 \theta\)[/tex] with 1 in the given equation:
[tex]\[
1 = x - 25
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Next, we need to isolate [tex]\(x\)[/tex]. To do this, add 25 to both sides of the equation:
[tex]\[
1 + 25 = x
\][/tex]
4. Simplify the expression:
Combine the constants on the left side:
[tex]\[
26 = x
\][/tex]
Hence, the value of [tex]\(x\)[/tex] is:
[tex]\[
x = 26
\][/tex]
So, the simplified form of the given equation leads us to:
[tex]\[
26 - x
\][/tex]
