wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

For 0<x<2, d(tan-1(1+cos121-cos12)dxis equal to


A

-14

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

14

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

-12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

-14


Explanation for the correct option :

Step1. Simplifying the given equation

Let, y=tan-11+cosx21-cosx2...(i) (1+cos2x)=2cos2x(1-cos2x)=2sin2x

Now using the above cos formula.

1+cosx2=2cos2x4&1-cosx2=2sin2x4

Insert this in equation (i)

Now,

y=tan-12cos2(x4)2sin2(x4)=tan-1cot2(x4)=tan-1[cot(π2-x4)=tan-1(tan(π2-x4))=π2-x4=-x4

Step3. Finding differentiation

Therefore, dydx=-14

Hence, correct option is (A)


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
L'hospitals Rule
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon