If cos x-y-cos x-y-m-n- then write the value of tan x tany-

We have, cos(x y)/cos(x+y)= m/n ⇒cosx cosy+sinx siny/cosx cosy sinx siny= m/n ⇒cosxcosy/cosxcosy+sinxsiny/cosxcosy/cosxcosy/cosxcosy sinxsiny/cosxcosy = m/n ⇒1+ ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

If cos x-y/co...

Question

If $\frac{c o s (x - y)}{c o s (x + y)} = \frac{m}{n}$ , then write the value of tanx tany.

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Solution

We have,
$\frac{c o s (x - y)}{c o s (x + y)} = \frac{m}{n}$
$\Rightarrow \frac{c o s x c o s y + s i n x s i n y}{c o s x c o s y - s i n x s i n y} = \frac{m}{n}$
$\Rightarrow \frac{\frac{c o s x c o s y}{c o s x c o s y} + \frac{s i n x s i n y}{c o s x c o s y}}{\frac{c o s x c o s y}{c o s x c o s y} - \frac{s i n x s i n y}{c o s x c o s y}} = \frac{m}{n}$
$\Rightarrow \frac{1 + t a n x t a n y}{1 - t a n x t a n y} = \frac{m}{n}$
$\Rightarrow n + n t a n x t a n y = m - m t a n x t a n y$
$\Rightarrow t a n x t a n y (n + m) = m - n$
$\Rightarrow t a n x t a n y = \frac{m - n}{m + n}$

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If cos(x−y)cos(x+y)=mn, then write the value of tanx tany.

We have, cos(x−y)cos(x+y)=mn ⇒cosxcosy+sinxsinycosxcosy−sinxsiny=mn ⇒cosxcosycosxcosy+sinxsinycosxcosycosxcosycosxcosy−sinxsinycosxcosy=mn ⇒1+tanxtany1−tanxtany=mn ⇒n+ntanxtany=m−mtanxtany ⇒tanxtany(n+m)=m−n ⇒tanxtany=m−nm+n

If $\frac{c o s (x - y)}{c o s (x + y)} = \frac{m}{n}$ , then write the value of tanx tany.