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
∑k = 16 sin2kπ7 - icos2kπ7 = ?
- 1
- i
i
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
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)
D.
Let z1 = cosA + isinA z2 = cosB + isinBand z3 = cosC + isinCThen, z1 = cosA - isinA z2 = cosB - isinBand z3 = cosC - isinCNow, if z = cosθ + isinθz= cosθ - isinθcosθ + isinθcosθ + isinθ = cos2θ + sin2θcosθ + isinθ = 1cosθ + isinθ = 1z
Now, z1 + z2 + z3 = cosA - isinA + cosB - isinB + cosC - isinC = cosA + cosB + cosC - isinA + sinB + sinC⇒ 1z1 + 1z2 + 1z3 = 0 ∵ z = 1z⇒ z1z2 + z2z3 + z3z1 = 0⇒ ∑cosA + isinAcosB + isinB = 0⇒ ∑cosAcosB - sinAsinB + sinAcosB + cosAsinB = 0⇒ ∑cosA + B + isinA + B = 0⇒ ∑cosA + B = 0 ∵ comparing the real part⇒ cosA + B + cosB + C + cosC + A = 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 = ?