Question
Download Solution PDFFind the value of the following expression.
5 (sin4 θ + cos4 θ) + 3(sin6 θ + cos6 θ) + 19sin2 θ cos2 θ
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
According to the question:
5 (sin4 θ + cos4 θ) + 3(sin6 θ + cos6 θ) + 19sin2 θ cos2 θ can be written as:
= 5 [(sin²θ + cos²θ)² - 2sin²θcos²θ] + 3[(sin²θ + cos²θ)³ - 3sin²θcos²θ(sin²θ + cos²θ)] + 19sin²θcos²θ
This can further be minimized as:
= 5 (1) - 10sin²θcos²θ + 3(1) - 9sin²θ cos²θ(1) + 19sin2θ cos2 θ
= 5 + 3 = 8
Hence, The Required value is 8.
Last updated on Jul 14, 2025
-> 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.