The most general solutions of the equation
secx - 1 = 2 - 1tanx are given by
nπ + π8
2nπ, 2nπ + π4
2nπ
None of these
If α + β - γ = π, then sin2α + sin2β - sin2γ is equal to
2sinαsinβcosγ
2cosαcosβcosγ
2sinαsinβsinγ
None of the above
The range of the function f (x) = Px - 37 - x is
{1, 2, 3}
{1, 2, 3, 4, 5, 6}
{1, 2, 3, 4}
{1, 2, 3, 4, 5}
The principal amplitude of sin40° + icos40°5 is
70°
- 110°
110°
- 70°
If the relation between direction ratios of two lines are given by a + b + c = 0 and 2ab + 2ac - bc = 0, then the angle between the lines is
π
2π3
π2
π3
The value of 2cos56°15' + isin56°15'8
- 16i
16i
8i
4i
If a = i^ - j^ + 2k^ and b = 2i^ - j^ + k^, then the angle θ between a and b is given by
tan-11
sin-112
sec-11
tan-113
C.
∵ cosθ = a1b1 + a2b2 + a3b3a12 + a22 + a32b12 + b22 + b32 = 1 × 2 + - 1 × - 1 + 2 × 11 + 1 + 44 + 1 + 1 = 2 + 2 + 26 = 66 = 1That means, θ = 0° or θ = 2π∵ sec2π = 1⇒ 2π = sec-11⇒ θ = sec-11
At t = 0, the function f(t) = sintt has
a minimum
a discontinuity
a point of inflexion
a maximum
If ∆r = 2r - 1Crm1m2 - 12mm + 1sin2m2sin2msin2m + 1, then the value of ∑r = 0m∆r
1
0
2
If cosα + isinα, b = cosβ + isinβ, c = cosγ + isinγ and bc + ca + ab = 1, then cosβ - γ + cosγ - α + cosα - β is equal to
32
- 32