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Pythagorean Identities

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

Level 1

         

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


Check out the set: 2016 Problems

True or False:

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

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

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

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

Evaluate \[\large { \begin{align} & \left(12 ^{\sin 24 ^\circ}\right)^{\sin 24 ^\circ} \times \left(12 ^{\sin 66 ^\circ}\right)^{\sin 66 ^\circ} \\ & \times \left(12 ^{\cos 36 ^\circ}\right)^{\cos 36 ^\circ} \times \left(12 ^{\cos 54 ^\circ}\right)^{\cos 54 ^\circ}. \end{align}}\]

Find the value of

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

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