1800-150-456-789
FlagBACK
Flag Discuss with Askiitians Tutors> the greatest value of the function f(x)=s...
question mark

the greatest value of the function f(x)=sin2x/sin(2x+pi/4) in the interval [0,pi/4] is
aans is root 2 plsssss explain

moidin afsan , 10 Years ago
Grade 11
anser 2 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans:
f(x) = \frac{sin2x}{sin(2x+\frac{\pi }{4})}
f(x) = \frac{sin2x}{sin(2x).cos(\frac{\pi }{4})+cos(2x).sin(\frac{\pi }{4})}
f(x) = \frac{\sqrt{2}sin2x}{sin(2x)+cos(2x)}
f'(x) = \sqrt{2}\frac{(sin2x+cos2x).(2cos2x)-sin2x(2cos2x-2sin2x)}{(sin(2x)+cos(2x))^{2}}f'(x) = \frac{2\sqrt{2}}{(sin(2x)+cos(2x))^{2}}> 0
=> f(x) is always increasing. So maxima of f(x) will be at x = pi/4.
f(\frac{\pi }{4}) = \frac{sin2.\frac{\pi }{4}}{sin(2.\frac{\pi }{4}+\frac{\pi }{4})}
f(\frac{\pi }{4}) = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

moidin afsan

Last Activity: 10 Years ago

thank uuuuuuuuuuu

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on discuss with askiitians tutors

question mark
Please send the full solution as soon as possible 🙏 
discuss with askiitians tutors
1 Answer Available

Last Activity: 2 Years ago

question mark
I got 80% in jee mains and am from sc category . Will i get a good NIT
discuss with askiitians tutors
1 Answer Available

Last Activity: 2 Years ago

question mark
Looking for an integrated JEE+NEET Coaching Classess for 2 years along with an ongoing normal syllabus related classes followed by regular revision tests, please.
Thanks
Gopinath [F/O Class 10th Student-Qatar]
discuss with askiitians tutors
0 Answer Available

Last Activity: 3 Years ago

question mark
Ntse coaching for class 9 ncert student, fee and schedule
discuss with askiitians tutors
1 Answer Available

Last Activity: 3 Years ago

question mark
Can a class 9 student take admission in the course, 2- what is the duration and mode of full course ie how many student in one class. 
discuss with askiitians tutors
0 Answer Available

Last Activity: 3 Years ago