Math / Trigonometry

Question $\sin^2 \theta + \left(\cos^2 \theta\right)\left(\cos^2 \theta\right)$

Studdy Solution

STEP 1

1. We are given a trigonometric expression involving $\sin^2 \theta$ and $\cos^2 \theta$ .
2. The expression can be simplified using trigonometric identities.

STEP 2

1. Simplify the expression \left(\cos^2 \theta\right)\left(\cos^2 \theta\).
2. Use trigonometric identities to further simplify the expression.

STEP 3

Simplify the term \left(\cos^2 \theta\right)\left(\cos^2 \theta\) by recognizing it as $(\cos^2 \theta)^2$ .
\left(\cos^2 \theta\right)\left(\cos^2 \theta\) = \cos^4 \theta

STEP 4

Substitute $\cos^4 \theta$ back into the original expression:
$\sin^2 \theta + \cos^4 \theta$

STEP 5

Recall the Pythagorean identity:
$\sin^2 \theta + \cos^2 \theta = 1$
However, in this case, we need to simplify $\sin^2 \theta + \cos^4 \theta$ . There isn't a direct identity to simplify this further without additional context or constraints, so this is the simplified form.
The expression $\sin^2 \theta + \cos^4 \theta$ is already in its simplest form given the information provided.

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