## If C=60° then show that a÷b+c + b÷c+a =1​

Question

If C=60° then show that a÷b+c + b÷c+a =1​

in progress 0
1 month 2021-08-17T21:24:28+00:00 2 Answers 0 views 0

## Answers ( )

=> 1/(a+c) + 1/(b+c) = 3 / ( a+b+c )

=> (a+b+2c) / (a+c) (b+c) = 3 / (a+b+c) =>(a+b+2c) (a+b+c) = 3(a+c) (b+c)

=> a^2 + b^2 + 2ab + 2c^2 + 3ac + 3bc = 3ab + 3ac + 3bc + 3c^2

=> a^2 + b^2 + 2ab – 3ab = 3 c^2 – 2 c^2 (cancel 3ac & 3bc)

=> a^2 + b^2 – ab = c^2

2. Step-by-step explanation:

What would you like to ask?

MATHS

If in a triangle ABC,∠C=60

, then prove that

a+c

1

+

b+c

1

=

a+b+c

3

Share

Study later

Formula:

c

2

=a

+

b

2

−2abcosC

Given, ∠C=60

∴c

2

=a

+

b

2

−2abcos60

c

2

=a

+

b

2

−ab…………..(1)

To prove:

a+c

1

+

b+c

1

=

a+b+c

3

a+c

1

+

b+c

1

=

a+b+c

3

(a+c)(b+c)

a+b+2c

=

a+b+c

3

(a+b+2c)(a+b+c)=3[(a+c)(b+c)]

a

2

+ab+ac+ba+b

2

+bc+2ca+2cb+2c

2

=3ab+3ac+3cb+3c

2

a

2

+b

2

+2ab−3ab=3c

2

−2c

2

a

2

+b

2

−ab=c

2

………….(2)

From (1) and (2) it’s clear that,

a+c

1

+

b+c

1

=

a+b+c

3