Let x1 and x2 be solutions of the equation sin-1x2 - 3x + 52 = π6. Then, the value of x12 + x22 is :
4
5
52
6
If α = cos-135, β = tan-113, where 0 < α, β < π2, then α - β is equal to :
tan-19510
tan-1914
sin-19510
cos-19510
If cos-1x - cos-1y2 = α, where - 1 ≤ x ≤ 1, - 2 ≤ y ≤ 2, x ≤ y2 then for all x, y, 4x2 - 4xycosα + y2 is equal to
4sin2α
2sin2α
4cos2α + 2x2y2
4sin2α - 2x2y2
A.
cos-1x - cos-1y2 = αLet cos-1x = A, cos-1y2 = Bx = cosA, y2 = cosBsinA = 1 - x2, sinB = 1 - y24xy2 + 1 + x21 - y24 = cosα1 - x2 - y24 + x2y24 = x2y24 + cos2α - xycosα4 - 4x2 - y2 = 4cos2α - 4 + 4cosα4x2 - 4xycosα + y2 = 4sin2α
y = logtanx2 + sin-1cosx, then dy/dx is
csc(x) - 1
cs(x)
csc(x) + 1
x
If 2tan-1cosx = tan-12cscx, then sinx + cosx is equal to
22
2
12
tan-13 - sec-1- 2csc-1- 2 + cos-1- 12 is equal to
45
- 45
35
0
If α and β are roots of the equation x2 + 5x - 6 = 0, then the value of tan-1α - tan-1β is
π2
π
π4
The value of cos-1cotπ2 + cos-1sin2π3 is
2π3
π3
The range of x for which the formula 3sin-1x = sin-1x3 - 4x2 hold is
- 12 ≤ x ≤ 12
- 14 ≤ x ≤ 23
- 13 ≤ x ≤ 1
- 23 ≤ x ≤ 23
The value of tan12cos-123 is
15
310
1 - 52