Trigonometry crush

Geometry Level 3

If in a non-equilateral triangle ABC, cosA + 2cosB + cosC = 2 , then a,b,c are in ?

none of these A.P H.P G.P

1 solution

Raj Rajput
Jul 25, 2015

Why can't it be GP?

Set A = B = C = 60 degrees. then a = b = c

Pi Han Goh - 5 years, 10 months ago

sorry sir i should mention that triangle is not equilateral

RAJ RAJPUT - 5 years, 10 months ago

Please do add that in the problem statement.

Pi Han Goh - 5 years, 10 months ago

a,b,c are angles of the triangle then how can you take sinA as A/k.

Can you mention what is k here and how it is the same k for different angles?(A,B,C)

Arent sinA,sinB,sinC in AP?

If sine are in AP can we say that the angles are in AP???

Nelson Mandela - 5 years, 10 months ago

small a,b,c are sides and Capital ones are angles of triangle

RAJ RAJPUT - 5 years, 10 months ago

Can you please justify the significance or value of k please?

Nelson Mandela - 5 years, 10 months ago

@Nelson Mandela – Sine rule : a/SinA = b/SinB = c/SinC = k ( any constant ). Here i have used k( any constant) just to convert angle form to side form as question was to find relationship amongst sides a,b,c .

RAJ RAJPUT - 5 years, 10 months ago

@Raj Rajput – from sine rule isnt k=2R where R is circumradius?

Nelson Mandela - 5 years, 10 months ago

@Nelson Mandela – Yes we can take that also but at last it has to be cancelled , so it doesn't matter what we take k or 2R . By the way you are right Here k=2R

RAJ RAJPUT - 5 years, 10 months ago

@Raj Rajput – Thanks and you have a very beautiful handwriting!

Nelson Mandela - 5 years, 10 months ago

@Nelson Mandela – Thanks :) :) :)

RAJ RAJPUT - 5 years, 10 months ago

Trigonometry crush

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