Home
Class 12
MATHS
In a triangle ABC, if a, b, c are in A.P...

In a triangle ABC, if a, b, c are in A.P. and `(b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2`, then find the value of sin B

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)`
`(b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2`
`rArr 2 sin B cos C + 2 sin C cos B + 2 sin B cos A + 2 sin B cos B = 2`
`rArr sin (B + C) + sin (A + B) = 1`
`rArr sin A + sin C = 1`
`rArr sin B = (1)/(2) " " ("As " 2 sin B = sin A + sin C)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.3|3 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

  • PROGRESSION AND SERIES

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

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC, if a,b,c are in A.P and (b)/(c)sin2C+(c)/(b)sin2B+(b)/(a)sin2A+(a)/(b)sin2B=2 then the value of sin B equals

In a Delta ABC , if A,B,C are in AP, then (a)/(c) sin2C+(c)/(a)(sin2A) is equal to

In triangle ABC if a, b, c are in A.P., then the value of (sin.(A)/(2)sin.(C)/(2))/(sin.(B)/(2)) =

In a /_\ABC , if A,B,C are in A.P., then: a/c (sin 2C) + c/a (sin 2A) = ....

In Delta ABC , if : a^(2), b^(2), c^(2) are in A.P., then : (sin 3B) : (sin B) =

In Delta ABC, if a,b,c are in A.P.then (2sin((A)/(2))sin((C)/(2)))/(sin((B)/(2)))=

In a triangle ABC, if 2b=a+c and A-C=90, then sin B equals

In any triangle ABC, show that: 2a sin((B)/(2))sin((C)/(2))=(b+c-a)sin((A)/(2))

A triangle ABC is such that sin(2A+B)=(1)/(2) and If A,B and C are in A.P.,then find the value of A and C

In a triangle ABC, prove that :a sin((A)/(2)+B)=(b+c)sin((A)/(2))