First slide

Trigonometric equations

Question

$I f \frac{1 - \tan x}{1 + \tan x} = \tan y a n d x - y = \frac{π}{6}, t h e n x, y a r e r e s p e c t i v e l y$

Moderate

A

$\frac{5 π}{24}, \frac{π}{24}$
B

$- \frac{7 π}{24}, - \frac{11 π}{24}$
C

$- \frac{115 π}{24}, - \frac{119 π}{24}$
D

all the above

Solution

$W e h a v e \tan (\frac{π}{4} - x) = \tan y = \tan (x - \frac{π}{6}) \{∵ x - y = \frac{π}{6}\}$
$∴ \frac{π}{4} - x = n π + x - \frac{π}{6} \Rightarrow (\frac{5 π}{12} - n π) = 2 x$
$\Rightarrow x = (5 - 12 n) \frac{π}{24} a n d y = x - \frac{π}{6}$
Options (1), (2), (3) correspond to n = 0, 1, 10 respectively .

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