The value of cos45°cos712°sin712° is
12
18
14
116
General solution of sinx + cosx = mina∈R1, a2 - 4a + 6 is
nπ2 + - 1nπ4
2nπ + - 1nπ4
nπ + - 1n + 1π4
nπ + - 1nπ4 - π4
If a= 22, b = 6, A= 45°, then
no triangle is possible
one triangle is possible
two triangles are possible
either no triangle or two triangles are possible
In a triangle ABC, if sinA sinB = abc2, then the triangle is
equilateral
isosceles
right angled
obtuse angled
The value of 1 + cosπ61 + cosπ31 + cos2π31 + cos7π6 is
316
38
34
If P = 12sin2θ + 13cos2θ then
13 ≤ P ≤ 12
P ≥ 12
2 ≤ P ≤ 3
- 136 ≤ P ≤ 136
A positive acute angle is divided into two parts whose tangents are 12 and 13. Then, the angle is
π4
π5
π3
π6
The smallest value of 5cosθ + 12 is
5
7
17
Show that
sinθcos3θ + sin3θcos9θ + sin9θcos27θ = 12tan27θ - tanθ
LHS = sinθcos3θ + sin3θcos9θ + sin9θcos27θNow, sinθcos3θ = sinθcos3θ × 2cosθ2cosθ= sin2θ2cos3θcosθ = 12sin3θ - θcos3θcosθ= 12sin3θcosθ - cos3θsinθcos3θcosθ= 12tan3θ - tanθSimilarly, sin3θcos9θ = 12tan9θ - tan3θand sin9θcos27θ = 12tan27θ - tanθ = RHS
The equation 3sinx + cosx = 4 has
infinitely many solutions
no solution
two solutions
only one solution