Question
Download Solution PDFयदि √7 sin θ = 3 cos θ, 0° < θ < 90° है, तो √(9 cosec²θ + 7 sec²θ) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
√7 sin θ = 3 cos θ
प्रयुक्त सूत्र:
cosec θ = 1/sin θ
sec θ = 1/cos θ
sin²θ + cos²θ = 1
गणना:
√7 sin θ = 3 cos θ
⇒ sin θ / cos θ = 3 / √7
⇒ tan θ = 3 / √7
⇒ sin²θ = 9 / (9 + 7) = 9/16
⇒ sin θ = 3/4
⇒ cosec θ = 4/3
cos²θ = 7 / 16
⇒ cos θ = √7 / 4
⇒ sec θ = 4 / √7
अब, √(9 x cosec²θ + 7 × sec²θ)
⇒ √(9 x (16/9) + 7 × (16/7))
⇒ √(16 + 16)
⇒ √32
⇒ 4√2
इसलिए, सही उत्तर 4√2 है।
Last updated on Apr 24, 2025
-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.
-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.
-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.
-> Eligible candidates can apply from 4th February 2025 to 5th March 2025.
-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.
-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.
-> Prepare for the exam with AAI Junior Assistant Previous year papers.