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

If A>0,B>0 and A+B=π3, then the maximum value of tanAtanBis


A

12

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

13

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

14

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

16

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

The correct option is B

13


Finding the value for tan open parentheses A close parentheses space tan open parentheses B close parentheses:

Given, A>0,B>0andA+B=π3

That means,tanA>0,tanB>0

We know that, AMGM

(tanA+tanB)2tan(A)tan(B)

(tanA+tanB)2tan(A)tan(B)

(tanA+tanB)-2tan(A)tan(B)=0

(tanA-tanB)2=0

tan(A)-tan(B)=0

tan(A)=tan(B)tan(A)=tan(B)

According to the given, this is possible when A=B

=π6

Therefore, tanAtanB=tanπ6tanπ6

=1313

=132

=13

Hence, option 'B' is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Range of Trigonometric Ratios from 0 to 90
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon