To determine the value of [tex]\(\sin^2 A + \cos^2 A\)[/tex] given that [tex]\(\tan A = \frac{3}{5}\)[/tex], we can proceed as follows:
1. Recall the Pythagorean Identity: One of the fundamental identities in trigonometry is:
[tex]\[
\sin^2 A + \cos^2 A = 1
\][/tex]
2. Given Information: We are provided with the value of [tex]\(\tan A\)[/tex]:
[tex]\[
\tan A = \frac{3}{5}
\][/tex]
3. Analysis: While the value of [tex]\(\tan A\)[/tex] is provided, it is not directly needed to calculate [tex]\(\sin^2 A + \cos^2 A\)[/tex]. The Pythagorean identity tells us that for any angle [tex]\(A\)[/tex], the sum of the squares of the sine and cosine of that angle is always 1.
Therefore, considering the identity, we conclude that:
[tex]\[
\sin^2 A + \cos^2 A = 1
\][/tex]
So, the value of [tex]\(\sin^2 A + \cos^2 A\)[/tex] is indeed [tex]\(1\)[/tex].
