Question
Download Solution PDFIf 2 cot θ = 3, then find the value of \(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
2cotθ = 3
Formula used:
Sinθ = P/H
Cosθ = B/H
Tanθ = P/B
Cotθ = B/P
H2 = P2 + B2
where P = Perpendicular
B = Base
H = Height
Calculation:
2cotθ = 3
⇒ cotθ = 3/2
on comparing with (Cotθ = B/P), we get
⇒ B = 3
⇒ P = 2
According to Pythagorean theorem
⇒ H2 = P2 + B2
⇒ H2 = 22 + 32
⇒ H = √13
⇒ Sinθ = 2/√13
⇒ Cosθ = 3/√13
⇒ Tanθ = 2/3
Putting all the values in the given equation:
\(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\)= (√13 * 2/√13 - 3 * 2/3 )/ (3 * 2/3 + √13 * 3/√13)
⇒ (2 - 2)/(2 + 3)
⇒ 0
The value of the expression is 0.
Last updated on Jul 10, 2025
-> The SSC CGL Application Correction Window Link Live till 11th July. Get the corrections done in your SSC CGL Application Form using the Direct Link.
-> 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.