Find the value of \(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 2)
View all SSC CGL Papers >
  1. sec 3θ - tan 3θ
  2. (sec 3θ - tan 3θ)3
  3. (sec 3θ - tan 3θ)2
  4. sec 3θ + tan 3θ

Answer (Detailed Solution Below)

Option 1 : sec 3θ - tan 3θ
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.3 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Calculation:

\(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)

⇒ By putting θ = 15° 

\(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)

⇒ \(\rm \sqrt{\frac{1-\sin 45}{1+\sin 45}} \)

⇒ \(\rm \sqrt{\frac{1-\ (1/\sqrt2)}{1+\ (1/\sqrt2)}} \) = \(\rm \sqrt{\frac{\sqrt2 \ - \ 1}{\sqrt2\ + \ 1}} \)

⇒ \(\rm \sqrt{\frac{\sqrt2 \ - \ 1}{\sqrt2\ + \ 1} \times\frac{\sqrt2 \ - \ 1}{\sqrt2\ - \ 1}} \)

⇒ \(\rm \sqrt{\frac{(\sqrt2 \ - \ 1)^2}{2-1}} \)

⇒ \(\rm \sqrt{(\sqrt2 \ - \ 1)^2}\)

⇒ √2 - 1

Again, In option 1  By putting θ = 15° we get,

sec 3θ - tan 3θ = sec 45° - tan 45°

⇒ √2 - 1

∴ The correct option is 1

Alternate Method

\(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)

⇒ \(\rm \sqrt{{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \times\frac{1-sin3\theta}{1-sin3\theta}} \)

⇒ \(\rm \sqrt{\frac{(1-\sin 3\theta)^2}{1^2-\sin^2 3\theta}} \)

⇒ \(\rm \sqrt{\frac{(1-\sin 3\theta)^2}{cos^2 3\theta}} \)

⇒ \(\rm \sqrt{(\frac{1-\sin 3\theta}{cos 3\theta}})^2 \)

⇒ \(\frac{1 - sin3\theta}{cos3\theta}\)

⇒ \(\frac{1}{cos3\theta}-\frac{sin3\theta}{cos3\theta}\)

⇒ sec 3θ - tan 3θ

∴ The correct option is 1

Latest SSC CGL Updates

Last updated on Jul 9, 2025

-> The SSC CGL Notification 2025 for the Combined Graduate Level Examination has been officially released on the SSC's new portal – www.ssc.gov.in.

-> Bihar Police Admit Card 2025 Out at csbc.bihar.gov.in

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The AP DSC Answer Key 2025 has been released on its official website.

-> The UP ECCE Educator 2025 Notification has been released for 8800 Posts.

Get Free Access Now
Hot Links: online teen patti real money teen patti master gold download teen patti app teen patti sequence online teen patti