Question

If 2sec x + 3tan x=7 then the value of 2tan x +3 sec x is

Answer 1

Gn that
$2 \sec(x) + 3 \tan(x) = 7$
ie Sq.on both sides
$4 { \sec(x) }^{2} + 9 { \tan(x) }^{2} + 12 \sec(x) \tan(x) = 4 - - - - - (1)$
Let

$4 { \tan(x) }^{2} + 9 { \sec(x) }^{2} + 12 \sec(x) \tan(x) = {a}^{2} - - - (2)$
(1)-(2)》
$2( { \sec(x) }^{2} - { \tan(x) }^{2} ) - 3( { \sec(x) }^{2} - { \tan(x) }^{2} ) = 49 - {a}^{2}$
ie
$- 1 = 49 - {x}^{2}$
ie
${x}^{2} = 50$
ie
$2 \tan(x) + 3 \sec(x) = plus(or)minus \: \: 5 \sqrt{2}$