Which of the following is the value of $\sqrt{\frac{1−sin 45°}{1+sin 45°}}$?

sec 45° − tan 45°

\(\sqrt { \frac{1 - sin45°}{1 + sin45°}\ }\)

= \(\sqrt { \frac{1 - 1/√2}{1 + 1/√2}\ }\)

= \(\sqrt { \frac{√2-1}{√2 + 1 }\ }\)

on rationalizing ,

= \(\sqrt { \frac{(√2-1) × (√2-1)  }{(√2 + 1) × (√2-1) }\ }\)

= \(\sqrt { \frac{(√2-1)²  }{ 2 - 1  }\ }\)

= (√2-1)

Now, By solving one by one for each option,

Option 4 :- sec 45° − tan 45°

= √2-1

( satisfied )

So,  Ans :-  sec 45° − tan 45°