The equation 3sin2x + 10cosx - 6 is satisfied, if
x = nπ ± cos-113
x = 2nπ ± cos-113
x = nπ ± cos-116
x = 2nπ ± cos-116
If ecosx - e- cosx = 4, then the value of cosx is
log2 + 5
- log2 + 5
log- 2 + 5
None of these
If tan-1ax + tan-1bx = π2, then x is equal to
ab
2ab
If cosθ - α = a, cosθ - β = b, then
sin2α - β + 2abcosα - β is equal to
a2 + b2
a2 - b2
b2 - a2
- a2 - b2
A.
Given, cosθ - α = a, cosθ - β = bWe have,α - β = θ - β - θ - α ...(i)∴ cosα - β = cosθ - βcosθ - α + sinθ - βsinθ - αand sinα - β = sinθ - βcosθ - α - sinθ - αcosθ - β⇒ cosα - β = b . a + 1 - a2 1 - b2and sinα - β = a 1 - b2 - b1 - a2Now, sin2α - β = a 1 - b22 + b1 - a22 - 2ab1 - a2 1 - b2⇒ sin2α - β = a21 - b2 + b21 - a2 - 2abcosα - β - ab⇒ sin2α - β + 2abcosα - β = a2 - a2b2 + b2 - b2a2 + 2a2b2⇒ sin2α - β + 2abcosα - β = a2 + b2
The most general solutions of the equation
secx - 1 = 2 - 1tanx are given by
nπ + π8
2nπ, 2nπ + π4
2nπ
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