Home
Class 12
MATHS
In a triangle ABC, prove that (b + c)/(a...

In a triangle ABC, prove that `(b + c)/(a) le cosec.(A)/(2)`

Text Solution

Verified by Experts

In the triangle ABC,
`(b + c)/(a) = (sin B + sin C)/(sin A)`
`= (2 sin.(B + C)/(2) cos.(B - C)/(2))/(2 sin.(A)/(2). Cos.(A)/(c))`
`= (cos.(B - C)/(2))/(sin.(A)/(2))`
`le (1)/(sin.(A)/(2))`
`rArr (b + c)/(a) le cosec. (A)/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.3|3 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Illustration|86 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

in any triangle ABC prove that (b-c)/acos^2(A/2)+(c-a)/(b)cos^2(B/2)+(a-b)(/c)cos^2(C/2)=0

In a triangle A B C prove that a/(a+c)+b/(c+a)+c/(a+b)<2

In any triangle ABC, prove that cosA + cos B + cos C le 3/2

In triangle ABC prove that tan((A+B)/2)=cot. C/2

In any triangle ABC, prove that, c sin((A-B)/2)= (a-b) cos( C/2)

In any triangle ABC, prove that, (b^(2)-c^(2))cot A + (c^(2)-a^(2)) cot B + (a^(2)-b^(2)) cot C=0

In any triangle ABC, prove that, (b-c)cot 'A/2' + (c-a) cot 'B/2' + (a-b) cot 'C/2'=0

For any triangle ABC prove that (b-c)cot(A/2)+(c-a)cot(B/2)+(a-b)cot(C/2) =0

In any triangle ABC, prove that, a^(3) cos(B-C) + b^(3) cos(C-A) + c^(3) cos(A-B) = 3abc.

In any triangle ABC, prove that (a^(2)sin(B-C))/(sin B + sinC) + (b^(2)sin(C-A))/(sinC + sinA) +(c^(2)sin(A-B))/(sinA + sinB)=0