Verify the trigonometric identity:

\[ \cos^2 \theta - \sin^2 \theta = 1 - 2\sin^2 \theta \]

⋮ s i n 2 θ + co s 2 θ = 1 → co s 2 θ = 1 − s i n 2 θ ⋮ co s 2 θ − s i n 2 θ = 1 − 2 s i n 2 θ L = co s 2 θ 1 − s i n 2 θ ​ ​ − s i n 2 θ = 1 − 2 s i n 2 θ = R L = R

Answered by Anonymous | 2024-06-10

To verify the trigonometric identity, we use the difference of squares and the Pythagorean identity, which results in the confirmation of the given identity.
To verify the trigonometric identity cos2θ - sin2θ = 1 - 2 sin2θ, we can use the difference of squares and the Pythagorean identity. The difference of squares for cosine and sine is cos2θ - sin2θ, which can also be written as 1 - sin2θ - sin2θ using the Pythagorean identity cos 2θ = 1 - sin 2θ. This simplifies to 1 - 2 sin2θ, confirming the original identity.

Answered by JunoTemple | 2024-06-24

To verify the identity cos 2 θ − sin 2 θ = 1 − 2 sin 2 θ , we substitute cos 2 θ using the Pythagorean identity. By simplification, both sides of the equation prove to be equal, confirming the identity is correct.
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Answered by Anonymous | 2024-12-20