If sin-1x + sin-11 - x = cos-1x, then x equals
1, - 1
1, 0
0, 1/2
None of these
Range of f(x) = sin-1x + tan-1x + sec-1x is
π4, 5π4
π4, 3π4
π4, 7π4
If 12sin-13sin2θ5 + 4cos2θ = tan-1x, then x is equal to
3cotθ
3tanθ
tan3θ
13tanθ
The value of 2tan-1csctan-1x - tancot-1x is
tan-1x
tanx
cotx
csc-1x
A.
2tan-1csctan-1x - tancot-1x= 2tan-1csccsc-11 + x2x - tantan-11x= 2tan-11 + x2x - 1x= 2tan-11 + x2 - xx= 2tan-1secθ - 1tanθ ∵ put x = tanθ= 2tan-11 - cosθsinθ = 2tan-12sin2θ22sinθ2 . cosθ2= 2tan-1tanθ2= 2 . θ2 = tan-1x
2tan-1cosx = tan-12cscx, then value of x is
3π4
π4
π3
The principal value of sin-1sin5π6 is
π6
5π6
7π6
Range of the function y = sin-1x21 + x2, is
0, π2
[0, π2)
(0, π2]
cos-1- 12 - 2sin-112 + 3cos-1- 12 - 4tan-1- 1 equals
19π12
35π12
47π12
43π12
x = cos-111 + t2, y = sin-111 + t2 ⇒ dydx is equal to
0
tan(t)
1
sin(t) cos(t)
The simplified expression of sin(tan-1(x)) for any real number x is given by