3 tanθ = \(2\sqrt 3 \) sinθ, 0° < θ < 90° అయితే, \(\rm \frac{{\cos e{c^2}2\,\theta + {{\cot }^2}2\,\theta }}{{{{\sin }^2}\,\theta + {{\tan }^2}2\,\theta }}\) విలువ:

This question was previously asked in
SSC CGL Tier 2 Quant Previous Paper 1 (Held On: 29 Jan 2022)
View all SSC CGL Papers >
  1. \(\frac{{20}}{{39}}\)
  2. \(\frac{{20}}{{27}}\)
  3. \(\frac{{4}}{{13}}\)
  4. \(\frac{{4}}{{3}}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{{20}}{{39}}\)
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

ఇచ్చిన సమస్య:

3 tanθ = \(2√ 3 \) sinθ

ఉపయోగించిన సూత్రం:

tanθ = \(\frac{sinθ }{{cosθ }}\)

cos 30° = \(\frac{√3}{{2}}\), cosec 60° = \(\frac{2}{{√3}}\)

Cot 60° = \(\frac{1}{{√ 3}}\), sin 30° = \(\frac{1}{{2}}\), tan 60° = √3

సాధన: 

3 tanθ = \(2√ 3 \) sinθ

⇒ 3 \(\frac{sinθ }{{cosθ }}\) = 2√3 sinθ 

⇒ \(\frac{3}{{cosθ }}\) = 2√3

⇒ cosθ = \(\frac{√3}{{2}}\) = cos 30° 

⇒ θ = 30° 

ఇప్పుడు,

\(\rm \frac{{\cos e{c^2}2\,θ + {{\cot }^2}2\,θ }}{{{{\sin }^2}\,θ + {{\tan }^2}2\,θ }}\) విలువ

⇒ \(\frac{cosec^2 60° + cot^2 60° }{{sin^2 30° + tan^2 60° }}\)   

⇒ \(\frac{(\frac{2}{{√3}})^2 \ + \ (\frac{1}{{√3}})^2} {(\frac{1}{{2}})^2 \ + \ (\sqrt3)^2}\)

⇒ \(\frac{\frac{4}{3} + \frac{1}{3}}{\frac{1}{4} + \frac{3}{1}}\) = \(\frac{\frac{5}{3} }{\frac{13}{4} }\)

⇒ \(\frac{{20}}{{39}}\)

∴ అవసరమైన విలువ \(\frac{{20}}{{39}}\).

Latest SSC CGL Updates

Last updated on Jul 8, 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.

-> 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.

-> Candidates should also use the SSC CGL previous year papers for a good revision. 

Get Free Access Now
Hot Links: teen patti master real cash teen patti real money app teen patti master old version teen patti gold new version teen patti 50 bonus