wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The inequality 2cosx1+sin2x1sin2x2 where x[0,2π] holds true in the interval [aπ2,bπ2]. Then the value of a+b is

Open in App
Solution

1+sin2x1sin2x=|cosx+sinx||cosxsinx|=2min{|cosx|,|sinx|}

Now,
2cosx2min{|cosx|,|sinx|}2cosxmin{|cosx|,|sinx|}12

Clearly, from the graph,
x[π4,7π4]a+b=12+72=4

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving Trigonometric Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon