If cos 2 B -cos A - C -cos A - C thenA- tan A- tan B- tan C are in A PB- tan A- tan B- tan C are in HPC- tan A- tan B- tan C are in A G PD- tan A - tan B - tan C are in GP

The correct option is D tanA, tanB, tanC are in GP cos2B = cos(A+C)/cos(A C) ⇒1 cos2B/1+cos2B = cos(A C) cos(A+C)/cos(A C) + cos(A+C) ⇒2sin^2B/2cos^2B = 2sin ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios for Sum of Two Angles

If cos 2 B =c...

Question

If $c o s 2 B = \frac{c o s (A + C)}{c o s (A - C)}$ then

tanA, tanB, tanC are in AP

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tanA, tanB, tanC are in GP

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tanA, tanB, tanC are in HP

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tanA, tanB, tanC are in AGP

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Solution

The correct option is B
tanA, tanB, tanC are in GP

$c o s 2 B = \frac{c o s (A + C)}{c o s (A - C)}$

$\Rightarrow \frac{1 - c o s 2 B}{1 + c o s 2 B} = \frac{c o s (A - C) - c o s (A + C)}{c o s (A - C) + c o s (A + C)}$

$\Rightarrow \frac{2 s i n^{2} B}{2 c o s^{2} B} = \frac{2 s i n A s i n C}{2 c o s A c o s C} \Rightarrow t a n A t a n C = t a n^{2} B$

$\Rightarrow$ tanA, tanB, tanC are in GP

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If cos2B=cos(A+C)cos(A−C) then

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