Geometry

Pythagorean Identities

Advanced Pythagorean Identities

         

What is the value of

sin210+sin220+sin230+sin240+sin250+sin260+sin270+sin280? \sin ^2 10 ^ \circ + \sin ^2 20 ^ \circ + \sin ^2 30 ^ \circ + \sin ^2 40 ^ \circ + \sin ^2 50 ^ \circ + \sin ^2 60 ^ \circ + \sin ^2 70 ^ \circ + \sin ^2 80 ^ \circ ?

If sinθ+cosθ=12 \sin \theta+ \cos \theta = \frac {1}{2} , what is the value of sinθcosθ \sin \theta \cos \theta ?

If sinθ+cosθ=12 \sin \theta+ \cos \theta = \frac {1}{2} , what is the value of sinθcosθ \sin \theta-\cos \theta ?

If sinθ+cosθ=12 \sin \theta+ \cos \theta = \frac {1}{2} , what is the value of tanθ+cotθ \tan \theta+\cot \theta ?

If tanθ+cotθ=3 \tan \theta+ \cot \theta = 3 , what is the value of sinθcosθ \sin \theta\cos \theta ?

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