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Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine. See more

\[\large \dfrac { { \tan }^{ 2 }\theta }{ { \tan }^{ 2 }\theta+ 1 }= \, ? \]

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**True or False**:

\[\large (\cos x - \sin x)(\cos x +\sin x) = \cos^4 x - \sin^4 x\]

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\[ {\sin}\theta+{\sin}^2\theta= 1\]

If the above equation is true, find the value of the expression below

\[ {\cos}^2\theta+{\cos}^4\theta. \]

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Find the value of

\[\cos^2 45^{\circ} +\sin^2 45^{\circ}.\]

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