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

In a right angled triangle, the sides are a,bandc with c as hypotenuse and c-b1,c+b1. Then, the value of (logc+ba+logc-ba)2logc+ba×logc-ba will be:


A

2

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

-1

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

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

1


Explanation for the correct option:

Finding the value of the expression:

As the given triangle is a right-angled triangle, with c as hypotenuse, so by applying Pythagoras Theorem, we get

c2=a2+b2c2-b2=a2...(1)

(logc+ba+logc-ba)2logc+ba×logc-ba=logalogc+b+logalogc-b2×logalogc+b×logalogc-b[logab=logbloga]=loga×logc+b+loga×logc-b2(loga)2=loga×logc2-b22(loga)2[loga+logb=log(ab),(a+b)(a-b)=(a2-b2)]=logc2-b22loga[logab=2loga]=loga2loga2=1

Hence, option D is correct.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Finding Ratio of Sides in Triangle when Angles are Given
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon