Question

if sin x + cos X = √2 then find the value of tan x + cos x.​

Answer 1

$\sin(x) + \cos(x) = \sqrt{2}$
Squaring both sides
${ \sin }^{2} x + { \cos }^{2} x + 2 \sin(x) \cos(x) = 2$
But
${ \sin }^{2} x + { \cos }^{2} x = 1$
hence
$2 \sin(x) \cos(x) = 1 \\ \sin(x) \cos(x) = \frac{1}{2}$
Hence

$\frac{1}{ \sin(x) \cos(x)} = 2$

Again
${ \sin }^{2} x + { \cos }^{2} x = 1$
Hence

=
$\frac{{ \sin }^{2} x + { \cos }^{2} x }{ \sin(x) \cos(x) } = 2$
$\frac{{ \sin }^{2} x }{ \cos(x) \sin(x) } + \frac{ { \cos }^{2} x }{ \sin(x) \cos(x) } = 2$
Hence
$\tan(x) + \cot(x) = 2$