In ABC- if r1- r2- r3 are in A-P- then A-2- B-2- C-2 are in

The correct option is D H.P. r_1, r_2, r_3 are in A.P. stanA2, stanB2, stan #10;C2 are in A.P. #10; #10; #10; #10; ∴ A2, B2, #10;C2 ...

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Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

In ABC, if ...

Question

In $△ A B C$ , if $r_{1}, r_{2}, r_{3}$ are in A.P., then $cot (A / 2), cot (B / 2), cot (C / 2)$ are in

A.P.

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G.P.

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H.P.

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None of these

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Solution

The correct option is D H.P.
$r_{1}, r_{2}, r_{3}$ are in A.P.
$⟹ s tan \frac{A}{2}, s tan \frac{B}{2}, s tan \frac{C}{2}$ are in A.P.

$∴ cot \frac{A}{2}, cot \frac{B}{2}, cot \frac{C}{2}$ are in H.P.

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Similar questions

Q. Assertion :In a

△ A B C

, if

a < b < c

and

r

is inradius and

r_{1}, r_{2}, r_{3}

are the axradii opposite to angle

A, B, C

respectively, then

r < r_{1} < r_{2} < r_{3}

Reason:

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

r

is the in-radius of the traingle

A B C

r_{1}, r_{2}, r_{3}

are in A.P. for the triangle

A B C

, then

cot (A / 2), cot (B / 2), cot (B / 2)

are in?

Q. If in a triangle ABC , (a - b) (s - c) = (b - c) (s - a), prove that

r_{1}, r_{2}, r_{3}

are in A.P

Q. If

a, c, d

are in A.P., then

r_{1}, r_{2}, r_{3}

are in

Q. Statement

- 1

: In a

Δ A B C

, if

a < b < c

and

r

is in-radius and

r_{1}, r_{2}, r_{3}

are the exradii opposite to angle

A, B, C

respectively, then

r < r_{1} < r_{2} < r_{3}

.

Statement

- 2

: For,

Δ A B C

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

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In △ABC, if r1,r2,r3 are in A.P., then cot(A/2),cot(B/2),cot(C/2) are in

The correct option is D H.P.r1,r2,r3 are in A.P.⟹stanA2,stanB2,stanC2 are in A.P. ∴cotA2,cotB2,cotC2 are in H.P.

In $△ A B C$ , if $r_{1}, r_{2}, r_{3}$ are in A.P., then $cot (A / 2), cot (B / 2), cot (C / 2)$ are in

The correct option is D H.P.
$r_{1}, r_{2}, r_{3}$ are in A.P.
$⟹ s tan \frac{A}{2}, s tan \frac{B}{2}, s tan \frac{C}{2}$ are in A.P.

$∴ cot \frac{A}{2}, cot \frac{B}{2}, cot \frac{C}{2}$ are in H.P.