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Geometry Level 1

cos ⁡ 2 3 4 ∘ + cos ⁡ 2 5 6 ∘ = ? \large \cos^2 34^\circ + \cos^2 56^\circ =\, ?

1.0 2.0 0.5 1.5

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Swapnil Das
Jul 6, 2016

  • cos ⁡ ( 90 − θ ) = sin ⁡ θ \cos { \left( 90-\theta \right) } =\sin { \theta }

  • cos ⁡ 2 θ + sin ⁡ 2 θ = 1 \cos ^{ 2 } \theta +\sin ^{ 2 }{ \theta } =1 ,

∴ \therefore cos ⁡ 2 3 4 ∘ + cos ⁡ 2 5 6 ∘ = cos ⁡ 2 3 4 ∘ + sin ⁡ 2 34 ∘ = 1 \cos^2 34^\circ + \cos^2 56^\circ =\cos ^{ 2 } 34^{ \circ }+\sin ^{ 2 }{ 34 } ^{ \circ }=1 .

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Munem Shahriar
Nov 27, 2017

cos ⁡ 2 3 4 ∘ + cos ⁡ 2 5 6 ∘ \cos^2 34^\circ + \cos^2 56^\circ

= cos ⁡ 2 3 4 ∘ + sin ⁡ 2 ( 9 0 ∘ − 5 6 ∘ ) = \cos^2 34^\circ + \sin^2(90^\circ - 56^\circ)

= cos ⁡ 2 3 4 ∘ + sin ⁡ 2 3 4 ∘ = \cos^2 34^\circ + \sin^2 34^\circ

= 1 = \boxed{1}

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