If x = secθ - cosθ, y = secnθ - cosnθ, then x2 + 4dydx2 is equal to
n2(y2 - 4)
n2(4 - y2)
n2(y2 + 4)
None of these
The two curves y = 3 and y = 5 intersect at an angle
tan-1log3 - log51 + log3log5
tan-1log3 + log51 - log3log5
tan-1log3 + log51 + log3log5
tan-1log3 - log51 - log3log5
The period of sin4x + cos4x is
π42
π22
π4
π2
If 3 cos x ≠ 2 sin x, then the general solution of sin2x - cos2x = 2 - sin2x is
nπ + - 1nπ2, n ∈ Z
nπ2, n ∈ Z
4n ± 1π2, n ∈ Z
(2n - 1)π, n ∈ Z
If cosx + cos2x = 1, then the value of sin12x + 3sin10x + 3sin8x + sin6x - 1, is equal to :
2
1
- 1
0
The product of all values of cosα + isinα3/5 is :
cosα + isinα
cos3α + isin3α
cos5α + isin5α
1 + cosπ81 + cos3π81 + cos5π81 + cos7π8 is equal to
12
18
cosπ8
14
If 3cosθ + sinθ = 2, then the value of θ is
nπ + - 1nπ4
- 1nπ4 - π3
nπ + π4 - π3
nπ + - 1nπ4 - π3
If in a AABC, (s - a)(s - b) = s(s - c) then angle C is equal to
90°
45°
30°
60°
The length of the shadows of a vertical pole of height h, thrown by the sun's rays at three different moments are h, 2h and 3h. The sum of the angles of elevation of the rays at these three moments is equal to
π3
π6
A.
In ∆ABC, tanα = ABBC = hh = 1⇒ tanα = tanπ4⇒ α = π4Now, in ∆ABD tanβ = ABBD = h2h⇒ tanβ = 12⇒ β = tan-112and in ∆ABE, tanγ = ABBE = h3h⇒ tanγ = 13⇒ γ = tan-113
∴ Required sum of angles = α + β + γ= π4 + tan-112 + tan-113= π4 + tan-112 + 131 - 12 × 13= π4 + tan-15656= π4 + tan-11= π4 + π4 = π2