Home
Class 12
MATHS
Prove that (cos C + cos A)/(c + a) + (co...

Prove that `(cos C + cos A)/(c + a) + (cos B)/(b) = (1)/(b)`

Text Solution

Verified by Experts

`(cos C + cos A)/(c + a) + (cos B)/(b)`
`= ((b cos C + c cos B) + (b cos A + a cos B))/(b(c + a))`
`= (a + c)/(b(c + a)) = (1)/(b)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.4|5 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.5|7 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|15 Videos

Similar Questions

Explore conceptually related problems

Prove that cos (A + B) cos (A - B) = cos^(2) B - sin^(2) A

If A + B + C = 180^(@) , prove that cos A + cos B - cos C = -1 + 4 cos (A)/(2) cos"" (B)/(2) sin"" (C )/(2)

In a Delta ABC, prove that a ( cos B + cos C) = 2 (b + c) sin^(2)""(A)/(2)

in a triangle ABC , ( cos A)/(a) = (cos B )/( b) = ( cos C )/( c ) if a=(1 )/( sqrt(6)) then the area of the triangle ( in square units ) is

Prove that cos (A + B) cos (A - B) = cos^(2) A - sin^(2) B = cos^(2) B- sin^(2) A

If A + B + C = 180^(@) , prove that sin A + sin B + sin C = 4 cos (A)/(2) cos"" (B)/(2) cos"" (C )/(2)

If in a triangle ABC, (1 + cos A)/(a) + (1 + cos B)/(b) + (1+ cos C)/(c) = (k^(2) (1 + cos A) (1 + cos B) (1 + cos C))/(abc) , then k is equal to

If Delta ABC is right triangle and if angleA = (pi)/(2) , then prove that cos B - cos C = -1 + 2 sqrt(2) cos"" (B)/(2) sin"" (C )/(2) .

Prove that b^(2) cos 2 A - a^(2) cos 2B = b^(2) -a^(2)

Prove that cos (A + B) cos C - cos (B + C) cos A = sin B sin (C - A)