If cos x-3 cos y then 2tan y-x - 2 us equal to

cos x=3cos y 2tan (y x2) =2sin (y x)cos (y x) =2sin ycos x sin xcos ycos y cos x+sin x sin y ⇒ 2 (1 tan x y y+tan x) ...

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Byju's Answer

Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

If cos x=3 ...

Question

If $cos x = 3 cos y$ then $2 tan \frac{y - x}{2}$ us equal to

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Solution

$cos x = 3 cos y$
$2 tan (\frac{y - x}{2})$
$= 2 \frac{sin (y - x)}{cos (y - x)}$
$= 2 \frac{sin y cos x - sin x cos y}{cos y cos x + sin x sin y}$
$\Rightarrow 2 (\frac{1 - tan x cot y}{cot y + tan x})$

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If cosx=3cosy then 2tany−x2 us equal to

cosx=3cosy2tan(y−x2)=2sin(y−x)cos(y−x)=2sinycosx−sinxcosycosycosx+sinxsiny⇒ 2(1−tanxcotycoty+tanx)

If $cos x = 3 cos y$ then $2 tan \frac{y - x}{2}$ us equal to

$cos x = 3 cos y$
$2 tan (\frac{y - x}{2})$
$= 2 \frac{sin (y - x)}{cos (y - x)}$
$= 2 \frac{sin y cos x - sin x cos y}{cos y cos x + sin x sin y}$
$\Rightarrow 2 (\frac{1 - tan x cot y}{cot y + tan x})$