sin x ⋅ cos x का अधिकतम मान क्या है?

This question was previously asked in
NDA (Held On: 6 Sep 2020) Maths Previous Year paper
View all NDA Papers >
  1. 2
  2. 1
  3. \(\dfrac{1}{2}\)
  4. \(2\sqrt{2}\)

Answer (Detailed Solution Below)

Option 3 : \(\dfrac{1}{2}\)
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
6 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

संकल्पना:

sin x का अधिकतम मान 1 है। 

cos x का अधिकतम मान 1 है। 

sin 2x = 2 sin x cos x

 

गणना:

निम्न ज्ञात करने के लिए: sin x ⋅ cos x का अधिकतम मान 

माना कि f(x) = sin x ⋅ cos x है। 

\(\rm = \dfrac{1}{2} \times (2\sin x \times \cos x) \\ = \dfrac{1}{2} \sin 2x\)

चूँकि हम जानते हैं, sin x का अधिकतम मान 1 है। 

इसलिए, sin 2x का अधिकतम मान 1 है। 

अतः f(x) का अधिकतम मान \(\dfrac{1}{2} \times 1 = \dfrac{1}{2}\)  है।  

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had 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. 

Get Free Access Now
Hot Links: dhani teen patti teen patti lotus online teen patti teen patti fun