The value of 1 + cosπ61 + cosπ31 + cos2π31 + cos7π6 is
316
38
34
12
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
The equation 3sinx + cosx = 4 has
infinitely many solutions
no solution
two solutions
only one solution
B.
We know that,
- a2 + b2 ≤ acosθ + bsinθ ≤ a2 + b2∴ - 3 + 1 ≤ 3sinx + cosx ≤ 3 + 1⇒ - 2 ≤ 3sinx + cosx ≤ 2But, 3sinx + cosx = 4
Thus, The given equation has no solution.
The value of
tanα + 2tan2α + 4tan4α + ... + 2n - 1tan2n - 1α + 2ncot2nα is
cot2nα
2ntan2nα
0
cotα
If tanαπ4 = cotβπ4, then
α + β = 0
α + β = 2n
α + β = 2n + 1
α + β = 2(2n + 1), ∀ n is an integer
The principal value of sin-1tan- 5π4 is
- π4
π2
- π2
The value of cosπ15cos2π15cos4π15cos8π15
116
- 116
1