Let-a-b-c-be-the-sides-opposite-the-angles-A-B-and-C-respectively-of-a-ABC-Find-the-value-of-k-such-that-a-a-b-kc-b-cot-A-2-cot-B-2-k-cot-C-2-

Question Number 19243 by Tinkutara last updated on 07/Aug/17

Let a, b, c be the sides opposite the

angles A, B and C respectively of a

Δ ABC . Find the value of k such that

(a) a + b = k c

(b) \cot \frac{A}{2} + \cot \frac{B}{2} = k \cot \frac{C}{2} .

Commented by Tinkutara last updated on 08/Aug/17

Thank you very much Sir!

Commented by ajfour last updated on 07/Aug/17

Commented by ajfour last updated on 08/Aug/17

a + b = kc, from figure this means or

\Rightarrow (x + y) + (x + z) = k (y + z) \dots (i)

rcot \frac{A}{2} + rcot \frac{B}{2} = krcot \frac{C}{2}

\Rightarrow z + y = kx \dots (ii)

using (ii) in (i) :

2 x + kx = k (kx)

\Rightarrow k^{2} - k - 2 = 0

(k - 2) (k + 1) = 0

k = - 1, k = 2

For the case here, k = 2 .

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