Geometry

Pythagorean Identities

Pythagorean Identities: Level 1 Challenges

         

tan2θtan2θ+1=?\large \dfrac { { \tan }^{ 2 }\theta }{ { \tan }^{ 2 }\theta+ 1 }= \, ?


Check out the set: 2016 Problems

True or False:

(cosxsinx)(cosx+sinx)=cos4xsin4x\large (\cos x - \sin x)(\cos x +\sin x) = \cos^4 x - \sin^4 x

sinθ+sin2θ=1 {\sin}\theta+{\sin}^2\theta= 1

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

cos2θ+cos4θ. {\cos}^2\theta+{\cos}^4\theta.

Evaluate (12sin24)sin24×(12sin66)sin66×(12cos36)cos36×(12cos54)cos54.\large { \begin{aligned} & \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{aligned}}

Find the value of

cos245+sin245.\cos^2 45^{\circ} +\sin^2 45^{\circ}.

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