If in - ABC-tanA2-56 and tanC2-25- then a-b-c are in-

Given: tanA2=56 and tanC2=25 We have: tanA2tanC2=56×25 ⇒√((s b)(s c)s(s a))√((s a)(s b)s(s c))=13 ⇒s bs=13 ⇒ 3s 3b=s ⇒ a+c=2b Clearly, a,b, c are in A.P. ...

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Standard XII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

If in Δ ABC,t...

Question

If in $Δ A B C, tan \frac{A}{2} = \frac{5}{6}$ and $tan \frac{C}{2} = \frac{2}{5},$ then $a, b, c$ are in:

A . P .

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G . P .

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H . P .

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A . G . P .

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Solution

The correct option is A $A . P .$
Given: $tan \frac{A}{2} = \frac{5}{6}$ and $tan \frac{C}{2} = \frac{2}{5}$
We have: $tan \frac{A}{2} tan \frac{C}{2} = \frac{5}{6} \times \frac{2}{5} \Rightarrow \sqrt{\frac{(s - b) (s - c)}{s (s - a)}} \sqrt{\frac{(s - a) (s - b)}{s (s - c)}} = \frac{1}{3} \Rightarrow \frac{s - b}{s} = \frac{1}{3} \Rightarrow 3 s - 3 b = s \Rightarrow a + c = 2 b$
Clearly, $a, b, c$ are in $A . P .$

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Product of Trigonometric Ratios in Terms of Their Sum

Standard XII Mathematics

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If in ΔABC,tanA2=56 and tanC2=25, then a,b,c are in:

The correct option is A A.P.Given: tanA2=56 and tanC2=25 We have: tanA2tanC2=56×25⇒√(s−b)(s−c)s(s−a)√(s−a)(s−b)s(s−c)=13⇒s−bs=13⇒3s−3b=s⇒a+c=2b Clearly, a,b,c are in A.P.

If in $Δ A B C, tan \frac{A}{2} = \frac{5}{6}$ and $tan \frac{C}{2} = \frac{2}{5},$ then $a, b, c$ are in: