Home
Class 12
MATHS
Given a triangle A B C with sides a=7, b...

Given a triangle `A B C` with sides a=7, b=8 and c=5. Find the value of expression `(sinA+sinB+sinC)(cot A/2+cotB/2+cotC/2)`

Text Solution

Verified by Experts

`(sin A + sin B + sin C) (cot.(A)/(2) + cot.(B)/(2) + cot.(C)/(2))`
`= ((a)/(2R) + (b)/(2R) + (c)/(2R)) ((s(s -a))/(Delta) + (s(s-b))/(Delta) + (s(s -c))/(Delta))`
`= ((a + b+ c)/(2R)) ((s(3s - a - b -c))/(Delta))`
`= ((2s)/(2R)) ((s^(2))/(Delta)) = (s^(3))/(RDelta)`
`= (s^(3))/(R(abc)/(4R)) = (4s^(3))/(abc)`
`= (4((a + b+ c)/(2))^(3))/(abc) = (4((7 + 8 + 5)/(2))^(3))/(7 xx 8 xx 5) = (100)/(7)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 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

Given a triangle ABC with sides a=7,b=8 and c=5. Find the value of expression (sin A+sin B+sin C)(cot(A)/(2)+cot(B)/(2)+cot(C)/(2))

Given a trriangle ABC with sides a=7;b=8 and c=5 Find the value of expressions (sin A+sin B+sin C)((cot A)/(2)(cot B)/(2)(cot C)/(2))

In any triangle ABC, the side are a=7,b=5 and c=8. Find A.

Given a triangle ABC with sides a=7,b=8 and c=5. If the value of the expression (sum sin A)(sum(cot A)/(2)) can be expressed in the form (p)/(q) where p,q in N and (p)/(q) is in its lowest form find the value of (p+q)

In triangle ABC , if AB=2,BC=4 and AC=5, then the value of (sinA-sinB)/(sinC) is equal to

If A+B+C=pi , prove that : sinA+sinB+sinC= 4cos( A/2 )cos( B/2) cos(C/2)

If A+B+C=180 , prove that: sinA+sinB+sinC=4cosA/2cosB/2cosC/2

In a triangle ABC if a^(2)+b^(2)=101c^(2) then find the value of (cot C)/(cot A+cot B)