I've Told You The Answer Already

Geometry Level 1

Let sin x \sin x be the answer to this question. Find the value of cos x \cos x .

± 1 2 \pm \frac1{\sqrt2} ± 1 3 \pm \frac1{\sqrt3} ± 1 4 \pm \frac1{\sqrt4} ± 1 5 \pm \frac1{\sqrt5}

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5 solutions

Rishabh Jain
Mar 24, 2016

Since answer to this question is unique and we have to find cos x \cos x when answer is sin x \sin x . Therefore this is posible only when both are same: sin x = cos x \large \color{#D61F06}{\sin x}=\color{#3D99F6}{\cos x} 1 = sin 2 x + cos 2 x = 2 sin 2 x = 2 cos 2 x 1=\color{#D61F06}{\sin^2 x}+\color{#3D99F6}{\cos^2 x}=2\color{#D61F06}{\sin^2 x}=2\color{#3D99F6}{\cos^2 x} sin x = cos x = ± 1 2 \large \implies \color{#D61F06}{\sin x}=\color{#3D99F6}{\cos x}=\pm \dfrac{1}{\sqrt 2}

Moderator note:

Simple standard approach.

@Pi Han Goh LOL , nice way of asking!

Nihar Mahajan - 5 years, 2 months ago
Nihar Mahajan
Mar 24, 2016

sin x = cos x tan x = 1 sec x = 1 2 + 1 = ± 2 cos x = ± 1 2 \sin x=\cos x \Rightarrow \tan x=1 \Rightarrow \sec x = \sqrt{1^2+1}=\pm\sqrt{2} \Rightarrow \cos x=\pm\dfrac{1}{\sqrt{2}}

O R OR

sin 2 x + cos 2 x = 1 2 cos 2 x = 1 cos 2 x = 1 2 cos x = ± 1 2 \sin^2 x+ \cos^2 x = 1 \Rightarrow 2\cos^2 x =1 \Rightarrow \cos^2 x = \dfrac{1}{2} \Rightarrow \cos x = \pm\dfrac{1}{\sqrt{2}}

展豪 張
Mar 26, 2016

(Liked) This should be a logic question. Nice one!

Haha, why it should be in logic?

Pi Han Goh - 5 years, 2 months ago

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I did spend some time comprehend the question... I think this is something called 'self-reference'?

展豪 張 - 5 years, 2 months ago

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Yes, it's self-reference. But it's only in Logic if we want to decipher whether the statement is true or not. (See truth-tellers and liars )

Glad you liked this question! +1

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh Oic. A logic question with a geometry coat =D

展豪 張 - 5 years, 2 months ago

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@Pi Han Goh Same method...done ;)

展豪 張 - 5 years, 2 months ago

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@展豪 張

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh Santi santi cazorla

Rafi Davis - 5 years, 2 months ago

@Pi Han Goh Haha who's this guy?

展豪 張 - 5 years, 2 months ago

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@展豪 張 Haha no idea. I don't follow the football news.

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh Neither do I... I have just created this , inspired by your problem. Try it ;)

展豪 張 - 5 years, 2 months ago

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@展豪 張 You should try converting it to MCQ (that is, delete your question unfortunately, then post another one). Plus, replace "statement" with "person". Then the description will be more fluid!

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh You're right. A 'lying statement' just sounds weird...

展豪 張 - 5 years, 2 months ago

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@展豪 張 Hahah! no problem. When I first started posting logic problems, I didn't know how to phrase my questions as well....

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh I face the same problem when I am posting solutions too. English is not my mother language....

展豪 張 - 5 years, 2 months ago

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@展豪 張 Haha! In my country, everyone speaks broken English!

Pi Han Goh - 5 years, 2 months ago

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@Pi Han Goh Haha! New-species-English captured!

展豪 張 - 5 years, 2 months ago

@Pi Han Goh He plays for Arsenal

Rafi Davis - 5 years, 2 months ago

sin x = cos x : if : x = 45 , so : sin ( - 45 ) = - sin 45 , cos ( - 45 ) = cos 45 .

Harshit Mittal
Mar 24, 2016

Dude it was a good one. Good question

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