2 Views

Question : Which of the following is the value of $\sqrt{\frac{1-\sin 45^{\circ}}{1+\sin 45^{\circ}}}$?

Option 1: $\cos 45^{\circ} - \tan 45^{\circ}$

Option 2: $\tan 45^{\circ} - \sec 45^{\circ}$

Option 3: $\tan 45^{\circ}$

Option 4: $\sec 45^{\circ} - \tan 45^{\circ}$


Team Careers360 6th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

Correct Answer: $\sec 45^{\circ} - \tan 45^{\circ}$


Solution : $\sqrt{\frac{1-\sin 45^{\circ}}{1+\sin 45^{\circ}}}$
= $\sqrt{\frac{(1-\sin 45^{\circ})^2}{(1+\sin 45^{\circ})(1-\sin 45^{\circ})}}$
= $\sqrt{\frac{(1-\sin 45^{\circ})^2}{(1-\sin^2 45^{\circ})}}$
= $\sqrt{\frac{(1-\sin 45^{\circ})^2}{\cos^2 45^{\circ}}}$
= $\frac{1-\sin 45^{\circ}}{\cos 45^{\circ}}$
= $\sec 45^{\circ} - \tan 45^{\circ}$
Hence, the correct answer is $\sec 45^{\circ} - \tan 45^{\circ}$.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books