A geometry problem by Mohammad Khaza

Geometry Level 2

If cos ⁡ A = 1 2 \cos A =\frac 1{\sqrt 2} , then cos ⁡ 2 A = ? \cos 2A=?


The answer is 0.

Mohammad Khaza by Mohammad Khaza , 20, Bangladesh

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3 solutions

Mohammad Khaza
Jun 24, 2017

cos90=0 , cos2A=cos(45x2)=cos90=0

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Hana Wehbi
Jun 26, 2017

cos ⁡ 2 A − sin ⁡ 2 A = cos ⁡ 2 A = ( 1 2 ) 2 − ( 1 2 ) 2 = 0 \cos^2 A - \sin^2A = \cos 2A =( \frac{1}{\sqrt{2}})^2- (\frac{1}{\sqrt{2}})^2= 0

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Maximos Stratis
Jun 26, 2017

From the double-angle formula:
cos ⁡ 2 A = 2 cos ⁡ 2 A − 1 = 2 ( 1 2 ) 2 − 1 = 2 1 2 − 1 = 1 − 1 = 0 \cos{2A} = 2 \cos^2{A} - 1 = 2 (\frac{1}{\sqrt{2}})^2 - 1 = 2 \frac{1}{2} - 1 = 1 - 1 = 0

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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