Home
Class 12
MATHS
If the angles A, B and C of a triangle a...

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression `(a)/(c) sin 2C + (c)/(a) sin 2A` is

A

`(1)/(2)`

B

`(sqrt3)/(2)`

C

1

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
Since angles of `DeltaABC` are in A.P., `2B = A +C`
Also, `A + B + C = 180^(@)`
`:. B = 60^(@)`
`:. (a)/(c) sin 2C + (c)/(a) sin 2A = 2 sin A C + 2 sin C cos A = 2 sin (A +C) = 2 sin B = 2 xx (sqrt3)/(2) = sqrt3`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Main Previous Year|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

The angles of a triangle ABC, are in Arithmetic progression and if b : c = sqrt(3) : sqrt(2), "find "angleA

If a, b and c represent the lengths of sides of a triangle then the possible integeral value of (a)/(b+c) + (b)/(c+a) + (c)/(a +b) is _____

In a triangle ABC , if a,b,c are the sides opposite to angles A , B , C respectively, then the value of |{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}| is

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If a ,b ,and c are the sides of a triangles and A , B and C are the angles opposites to a ,b and c , respectively then "Delta"=|a^2b s in A c s in A bs in A1cos A cs in A cos A1| is independent of

If angle C of triangle ABC is 90^0, then prove that tanA+tanB=(c^2)/(a b) (where, a , b , c , are sides opposite to angles A , B , C , respectively).