If sinθ + cosθ = p and sin3θ + cos3θ = q, then p(p2 - 3) is equal to
q
2q
- q
- 2q
The set of solutions of the system of equationsx + y = 2π3and cosx + cosy = 32,where x, y are real, is
x, ycosx - y2 = 12
x, ysinx - y2 = 12
x, ycosx - y = 12
Empty set
If in the angles of a triangle are in the ratio1 : 1 : 4, then the ratio of the perimeter of the triangle to its largest side is
2 + 2 : 3
3 : 2
3 + 2 . 2
2 + 3 : 3
If cosx = tany, coty = tanz and cotz = tanx then sinx = ?
5 + 14
5 - 14
5 + 12
5 - 12
D.
Given, cosx = tany, coty = tanz and cotz = tanx∴ cosx = tany⇒ cosx = 1tanz⇒ cosx = cotz⇒ cosxx = tanx⇒ cosx =sinxcosx⇒ cos2x = sin(x)⇒ 1 - sin2x = sinx⇒ sin2x - sinx - 1 = 0∴ sinx = - 1 ± 1 - 4 × - 12 × 1= - 1 ± 52∴ sinx = 5 - 12 ∵ - 1 - 52 < - 1
tan81° - tan63° - tan27° + tan9° = ?
6
0
2
4
If x and y are acute angles such that cos(x) + cos(y) = 32sin(x) + sin(y) = 34, then sin(x + y) equals to
25
34
35
45
The sum of the solutions in 0, 2π the equation cosxcosπ3 - xcosπ3 + x = 14 is
4π
π
2π
3π
In any ∆ABC, a + b + cb + c - ac + a - ba + b - c4b2c2 = ?
sin2B
cos2A
cos2B
sin2A
If ssinθ + cosθ = p and tanθ + cotθ = q, then q(p2 - 1) is equal to
12
1
3
tanπ5 + 2tan2π5 + 4cot4π5 is equal to
cotπ5
cot2π5
cot3π5
cot4π5