Question
Download Solution PDF(1 + cot θ - cosec θ)(1 + tan θ + sec θ) దేనికి సమానం?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFభావన:
త్రికోణమితి సూత్రం
cot θ = \(\rm \frac{cos θ }{sin θ }\)
tan θ = \(\rm \frac{sin θ }{cos θ }\)
cosec θ = \(\rm \frac{1 }{sin θ }\)
sec θ = \(\rm \frac{1}{cos θ }\)
sin2 θ + cos2 θ = 1
(sin θ + cos θ)2 = sin2 θ + cos2 θ + 2 sin θ cos θ
లెక్కింపు:
(1 + cot θ - cosec θ)(1 + tan θ + sec θ) యొక్క విలువ కనుగొనడానికి:
= (1 + \(\rm \frac{cos θ }{sin θ }\) - \(\rm \frac{1 }{sin θ }\) (1 + \(\rm \frac{sin θ }{cos θ }\) + \(\rm \frac{1}{cos θ }\)
\(\rm \frac{(sin θ + cos θ - 1) ( sin θ + cos θ + 1)}{sin θ \: cosθ }\)
\(\rm \frac{( sin θ + cos θ )^{2} - 1}{ sin θ cos θ }\)
\(\rm \frac{sin^{2}θ + cos^{2}θ + 2 sin θ cos θ - 1}{sinθ \: cos θ }\)
= \(\rm \frac{1 + 2 sin θ cos θ - 1}{sinθ \: cos θ }\)
= \(\rm \frac{2 sin θ cos θ }{sinθ \: cos θ }\)
= 2
Last updated on Jun 18, 2025
->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.