CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that
(tanA-tanB)2 + (1+tanAtanB)2
is equal to sec square A*sec squareB

Open in App
Solution

Taking L.H.S. , we have
LHS = (1 + tan a tan b)2 + (tan a – tan b)2
= 1 + tan2a tan2b + 2 tan a tan b + tan2a + tan2b – 2 tan a tan b
= 1 + tan2a tan2b + tan2a + tan2b
= 1. (1 + tan2b) + tan2a (tan2b + 1)
= (1 + tan2b) + (1 + tan2a)
= sec2b sec2a
= sec2a sec2b
= RHS

flag
Suggest Corrections
thumbs-up
10
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Standard Values of Trigonometric Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon