A geometry problem by Chris San

Geometry Level 1

True or false :

\quad cos ( ω ) = cos ω \cos (-\omega) = \cos \omega .

False True

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1 solution

Aditya Sky
Mar 27, 2016

cos ( θ ) \cos(\theta) is an even function which means c o s ( θ ) = cos ( θ ) \color{#D61F06}{cos(-\theta)=\cos(\theta)} .

Simple Proof :- \huge \color{#3D99F6}{\text{Simple Proof :-}}

cos ( θ ) = cos ( 0 θ ) = cos ( 0 ) 1 cos ( θ ) + sin ( 0 ) 0 sin ( θ ) . . . . . . . . . . cos ( α β ) = cos ( α ) cos ( β ) + sin ( α ) sin ( β ) \cos(-\theta)\,=\,\cos(0-\theta)\,=\, \underbrace{\cos(0)}_\text{1} \cdot \cos(\theta)\,+\,\underbrace{\sin(0)}_\text{0} \cdot \sin(\theta) \,\,..........\,\,\color{#624F41}{\cos(\alpha-\beta)=\cos(\alpha) \cdot \cos(\beta)\,+\, \sin(\alpha) \cdot \sin(\beta) } Hence, cos ( θ ) = cos ( θ ) \color{#20A900}{\cos(-\theta)\,=\,\cos(\theta)}

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