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

If y=1+tanA1-tanB, where A-B=π4, then y+1y+1 is equal to


A

9

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

4

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

27

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

81

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

The correct option is C

27


Explanation for the correct option.

Step 1. Find the value of y.

It is given that A-B=π4. So we take tan on both sides:

tanA-B=tanπ4tanA-tanB1+tanAtanB=1tanA-tanB=1+tanAtanB...(1)

Now expand the expression y=1+tanA1-tanB

y=1+tanA1-tanBy=1-tanB+tanA-tanAtanBy=(tanA-tanB)+(1-tanAtanB)

Using the equation (1) substitute 1+tanAtanB for tanA-tanB.

y=1+tanAtanB+1-tanAtanB=1+1=2

Step 2. Find the value of the given expression.

In the expression y+1y+1 substitute 2 for y and simplify.

y+1y+1=2+12+1=33=27

So, the value of the given expression is 27.

Hence, the correct option is C.


flag
Suggest Corrections
thumbs-up
37
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebra of Derivatives
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon