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Complete the proof of the identity by choosing the Rule that justifies each step.

cos^(2)x-sin^(2)x=1-2sin^(2)x
To see a detailed description of a Rule, select the More Information Button to the

Complete the proof of the identity by choosing the Rule that justifies each step. $\newline$ $\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$ $\newline$ To see a detailed description of a Rule, select the More Information Button to the

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Solve equations using a quadratic pattern

Full solution

Q. Complete the proof of the identity by choosing the Rule that justifies each step.

\newline

\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x

\newline

To see a detailed description of a Rule, select the More Information Button to the

Replace with Pythagorean identity: We start with the left side of the equation: $\cos^2 x - \sin^2 x$ . We know from the Pythagorean identity that $\cos^2 x + \sin^2 x = 1$ . Therefore, we can replace $\cos^2 x$ with $1 - \sin^2 x$ in our original equation.
Combine like terms: Now we have $(1 - \sin^{2}x) - \sin^{2}x$ . We simplify this by combining like terms. This results in $1 - 2\sin^{2}x$ .
Complete the proof: We have now shown that $\cos^2 x - \sin^2 x$ simplifies to $1 - 2\sin^2 x$ . This completes the proof of the identity.

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