In a triangle A B C , if cos A+2\ cos B+...

In a triangle `A B C ,` if `cos A+2\ cos B+cos C=2.` prove that the sides of the triangle are in A.P.

Text Solution

AI Generated Solution

Topper's Solved these Questions

PERMUTATIONS AND COMBINATIONS
ALLEN|Exercise All Questions|1 Videos
Solutions of Triangle & Binomial Theorem
ALLEN|Exercise Do yourself -6|4 Videos

Similar Questions

Explore conceptually related problems

If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the triangle are in AP

In a triangle ABC, a (b cos C - c cos B) =

If in a triangle ABC, cos A +cos B+cos C=3/2 , prove that the triangle is equilateral.

In a triangle ABC, cos A+cos B+cos C=

In triangle ABC, if cos^(2)A + cos^(2)B - cos^(2) C = 1 , then identify the type of the triangle

In a triangle ABC cos^(2)A/2+cos^(2)B/2+cos^(2)C/2=

If cos A+cos B+2cos C=2 then the sides of the A B C are in (a)A.P. (b) G.P. (c) H.P. (d) none

If in a triangle A B C ,acos^2(C/2)+ c cos^2(A/2)=(3b)/2, then the sides a ,b ,a n dc are in A.P. b. are in G.P. c. are in H.P. d. satisfy a+b=cdot

In a Delta ABC , cos (A + B) + cos C =

In a triangle A B C , if cos A=(sinB)/(2sinC) , show that the triangle is isosceles.

ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions

If b , c , B are given and b &lt c,prove that cos((A1-A2)/2)=(csinB)/b
Text Solution
|
If in a triangle ABC, cos A +cos B+cos C=3/2, prove that the triangle ...
Text Solution
|
In a triangle A B C , if cos A+2\ cos B+cos C=2. prove that the sides ...
Text Solution
|
In a triangle A B C\ a : b : c=sqrt(3)\ :1\ :\ 1, then the triangle is...
Text Solution
|
The sides of a triangle A B C are x , y ,\ sqrt(x^2+y^2+x y) respectiv...
Text Solution
|
In a "Delta"A B C\ ((a^2)/(sinA)+(b^2)/(sinB)+(c^2)/(sinC))dotsinA/2si...
Text Solution
|
If p1, p2, p3, be the altitudes of a triangle ABC from the vertices A,...
Text Solution
|
If in a triangle A B C angle B=90^0 then tan^2(A/2) is (b-c)/a (b) (b-...
Text Solution
|
In a triangle A B C ,\ If (a^3+b^3+c^3)/(sin^3A+sin^3B+sin^3C)=343 , ...
Text Solution
|
In a Delta ABC if b+c = 3a then cot. (B)/(2). cot. (C )/(2) has the va...
Text Solution
|
If a/(sinA)=K , then the area of "Triangle ABC" in terms of K and sine...
Text Solution
|
In a triangle A B C ,/c=60^0a n d/A=75^0 . If D is a point on A C such...
Text Solution
|
In a ΔABC, a semicircle is inscribed, whose diameter lies on the side ...
Text Solution
|
In a triangle A B C , right angled at B , then r=(A B+B C-A C)/2 b. r=...
Text Solution
|
In triangle A B C where A ,\ B ,\ C are acute, the distances of the or...
Text Solution
|
In a Delta ABC, show that (a cos A+b cos B+ c cos C)/(a+b+c)= (r )/(R...
Text Solution
|
In an equilateral triangle, the inradius, circumradius, and one of the...
Text Solution
|
Show that ((1)/(r (1))+ (1)/(r(2)))((1)/(r(2))+(1)/(r (3)))((1)/(r (3)...
Text Solution
|
In a triangle A B C ,(r1+r2)/(1+cosC) is equal to (2a b)/(c"Delta") (b...
Text Solution
|
With usual notations in a triangle A B C , if r1=2r2=2r3 then 4a=3b (b...
Text Solution
|