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
The value of
tanα + 2tan2α + 4tan4α + ... + 2n - 1tan2n - 1α + 2ncot2nα is
cot2nα
2ntan2nα
0
cotα
D.
Now, 2ntan2nα + 2ncot2nα= 2n - 1sin2n - 1αcos2n - 1α + 2cos2nαsin2nα= 2n - 1cos2nαcos2n - 1α + sin2nαsin2n - 1α + cos2nαcos2n - 1αsin2nαcos2n - 1α= 2n - 1cos2n - 1α1 + cos2nαsin2nαcos2n - 1α= 2n - 1cot2n - 1α
Proceeding in similar way in last, we get
tanα + 2cot2α
= sinαcosα + 2cos2αsin2α= cos2αcosα + sin2αsinα + cos2αcosαsin2αcosα= cosα1 + cos2α2sinαcos2α= 2cosα2sinα= cosαsinα= 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