Question
Download Solution PDFIf A is an acute angle, the simplified form of
\(\rm \frac{{\cos (\pi - A).\cot \left( {\frac{\pi }{2} + A} \right)\cos ( - A)}}{{\tan (\pi + A)\tan \left( {\frac{{3\pi }}{2} + A} \right)\sin (2\pi - A)}}\)is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
Formula used:
- cos (π - θ) = - cos θ
- cot (90 + θ) = - tan θ
- cos (-θ) = cos θ
- tan (π + θ) = tan θ
- tan (3π/2 + θ) = - cot θ
- sin (2π - θ) = - sin θ
Calculation:
\(\rm \frac{{\cos (π - A).\cot \left( {\frac{π }{2} + A} \right)\cos ( - A)}}{{\tan (π + A)\tan \left( {\frac{{3π }}{2} + A} \right)\sin (2π - A)}}\)
By using the above formula
\(\rm \frac{{\ (-cos A)\ . \ ( {-tan A} )\ \ .\ cos A}}{{\tan A\ .\ (-cot A ).\ (-sin A)}}\)
⇒ \(\frac{cos A\ .\ cos A}{cot A\ . \ sin A}\)
But, cos θ / sin θ = cot θ
⇒ cot A. cos A/ cot A
⇒ cos A
∴ The correct answer is cos A.
Last updated on Jul 12, 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.
-> The RRB Railway Teacher Application Status 2025 has been released on its official website.
-> The OTET Admit Card 2025 has been released on its official website.