If sin(A) + sin(B) + sin(C) = 0 and cos(A) + cos(B) + cos(C) = 0, then cos (A + B) + cos (B + C) + cos(C + A) is equal to
cos(A + B + C)
2
1
0
If tanθ . tan120° - θtan120° + θ = 13, then θ is equal to
nπ3 + π18, n ∈ Z
nπ3 + nπ12, n ∈ Z
nπ12 + π12, n ∈ Z
nπ3 + π6, n ∈ Z
1 + cosπ8 - isinπ81 + cosπ8 + isinπ88 = ?
- 1
12
If 1 + tanα1 + tan4α = 2, α ∈ 0, π16,then α = ?
π20
π30
π40
π50
If cosθ = cosα - cosβ1 - cosαcosβ, then one of the values of tanθ2 is
cotβ2tanα2
tanα2tanβ2
tanβ2cotα2
tan2α2tan2β2
The value of the expression 1 + sin2αcos2α - 2πtanα - 3π4 - 14sin2αcotα2 + cot3π2 + α2 is
sin2α2
sin2α
In ∆ABC if x = tanB - C2tanA2, y = tanC - A2tanB2 and z = tanA - B2tanC2, then x + y + z = ?
xyz
- xyz
2xyz
12xyz
If A > 0, B > 0 and A + B = π3, then the maximum value of AtanB is
13
3
B.
Let y = tanAtanBy = tanAtanπ3 - A ∵ A + B = π3⇒ dydA = sec2Atanπ3 - A - sec2π3 - AtanAFor maxima or minima, put dydA = 0∴ sec2Atanπ3 - A = tanAsec2π3 - A⇒ 1 + tan2Atanπ3 - A = tanA1 + tanπ3 - A⇒ tanπ3 - A + tan2Atanπ3 - A = tanA + tanA tan2π3 - A⇒ tanπ3 - A - tan A1 - tanAtanπ3 - A = 0⇒ tanπ3 - A = tanA⇒ π3 - A = A ⇒ 2A = π3⇒ A = π6Maximum value of tanAtanB = tanπ6tanπ6= 13 × 13 = 13
In ∆ABC, if bcosθ = c - a, (where θ is an acute angle), then (c - a) tanθ = ?
2cacosB2
2acsinB2
2casinB2
If tanα and tanβ are the roots of the equation x2 + px + q = 0, then the value ofsin2α + β + pcosα + βsinα + β + qcos2α + β
p + q
p
q
pp + q