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

Inverse circular functions,Principal values of sin1x,cos1x,tan1x.
tan1x+tan1y=tan1x+y1xy, xy<1
π+tan1x+y1xy, xy>1.
(a) sin1(1x)2sin1x=π/2.
(b) If sin1x+sin1(1x)=cos1x, then prove that x is equal to 0,1/2.

Open in App
Solution

(a) The given equation can be written as
sin1(1x)=π/2+2sin1x
Taking sine, we get
1x=cos(2sin1x)=12(sinsin1x)2
or 1x=122x or x=2x2
x=0 or 1/2,
A check shows that x=1/2 is not a root.
Hence x=0 is the only root.
(b) sin1[x1(1x)2+(1x)(1x2)]=sin11x2
x2xx2=1x2[1(1x)]=x1x2
x=0 or 2xx2=1x2 or x=1/2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Inverse Trigonometric Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon