Let a, b, c, d be numbers in the interval [0, π] such that sina + 7sinb = 4(sinc + 2sind) cosa + 7cosb = 4(cosc + 2cosd) Prove that 2cos(a – d) = 7cos(b – c)
My Self Assessment
Solve the equation cos2x + cos22x +cos23x = 1
a)
b)
c)
d) All of the above
Prove that
Let . For k = 1, 2, . . ., find for all real numbers x.
d)
In a triangle ABC, 3sinA + 4cosB = 6 and 4sinB + 3cosA = 1. Find the measure of angle C.
(4cos29° − 3) (4cos227° − 3) =
a) sin9°
b) cos9°
c) tan9°
d) cot9°
Let ABC be a triangle.
a) 0
b) 1
c) tan2A + tan2B + tan2C
d) tanA tanB tanC
Let ABC be a triangle. cos2A + cos2B + cos2C +2cosa cosB cosC
Prove that for all where k ε Z
(1 + tan1°)(1 + tan2°). . . . (1 + tan45°) =
a) 221
b) 222
c) 223
d) 245
If , sin23α – sin2α =
a) sinα sin3α
b) cosα cos3α
c) sin2α sin3α
d) cos2α cos3α
If , cosec2α + cosec4α =
a) sinα
b) cosecα
c) cosα
d) secα
If , cosα is a root of
a) x3 - 4x2 + 4x – 8 = 0
b) x3 + 4x2 – 4x + 8 = 0
c) 8x3 - 4x2 – 4x + 1 = 0
d) 8x3 + 4x2 – 4x – 1 = 0
If , cosα – cos2α + cos3α =
d) 1
Prove that Hence or otherwise evaluate the integral .
If the expression is real then the set of all possible values of x is . . . .
a) x = 2nπ or mπ + π/4
b) x = nπ or mπ + π/4
c) x = 2nπ or 2mπ + π/4
d) x = nπ or 2mπ + π/4
Does the equation |sinx| = sinx + 3 have any roots?
a) No roots
b) One root
c) Two roots
d) ∞ roots
Does the equation |tanx| = tanx + 3 have any roots in [0, 2π]?
b) Has roots in
c) Has roots in
d) Has roots in
The value of cot is
If sin-1 + cosec-1 =
Then the value of x is
a) 1
b) 3
c) 4
d) 5
The number of values of x in the interval [0, 3π] satisfying the equation 2sin2x + 5sinx – 3 = 0 is
a) 6
c) 2
d) 4
If 0 < x < π and cos x + sin x = then tan x is
In a triangle PQR, angle R = . If tan and tan are roots of ax2 + bx + c = 0, a ≠ 0 then
a) b =a + c
b) b = c
c) c = a + b
d) a = b + c
In a triangle ABC, let angle C = . If r is the inradius and R is the circumradius of the triangle ABC then 2(r + R) equals
a) c + a
b) a + b + c
c) a + b
d) b + c
