Question
Download Solution PDFFind the value of \(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
\(\rm \sqrt{\frac{1-\sin 3\theta}{1+\sin 3\theta}} \)
⇒ 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
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.