Question

cos C
if P. p2.ps are the lengths of the altitudes of a triangle from the vertices A.B.C. then cos A
cos B
+
+
B
R
(C)
cot A-cot B-cocc
(D) 2R​

Answer 1

Answer:

....................

Answer 2

Answer:

• Hope this you

Step-by-step explanation:

What would you like to ask?

MATHS

If p

1

,p

2

,p

3

are the altitudes of a triangle from the vertices A, B, C and △ , the area of the triangle, prove that

p

1

1

+

p

2

1

−

p

3

1

=

(a+b+c)△

2ab

cos

2

2

C

.

Share

Study later

ANSWER

Since p

1

,p

2

,p

3

are perpendiculars from the vertices A, B, C to the opposite sides, we have

△=

2

1

ap

1

=

2

1

bp

2

=

2

1

cP

3

Hence

p

1

1

+

p

2

1

p

3

1

=

2△

a

+

2△

b

−

2△

c

=

2△

a+b−c

=

2△

a+b+c−2c

=

2△

2s−2c

=

△

s−c

=

△s

ab

.

ab

s(s−c)

=

△s

ab

cos

2

2

1

C=

2

1

C=

(a+b+c)△

2ab

cos

2

2

1

C.