Trigonometric Equation Questions

Given A = sin2 θ + cos4 θ then for all real values of θ

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then...

The angle between the lines whose direction consines satisfy the equations l + m + n = 0 and l2 = m2 + n2 is

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45o. It flies off horizontally straight away from the point O. After one second, the elevati...

Let A and B be two events such that = , P(A ∩ B) = and P() = , where stands for the complement of the event A. Then the events A and B are...

Let fk(x) = (sink x + cosk x) where x ∈ R and k ≥ 1. Then f4(x) - f6(x) equals...

For x ∈ (0, π) the equation sinx + 2sin2x - sin3x = 3 has

The following integral (2 cosec x)17 dx is equal to

Two sides of a rhombus are along the lines, x – y + 1 = 0 and 7x – y  5 = 0. If its diagonals intersect at (–1, – 2), then which one of the following is a vertex of this rhombus?

The integral ∫sin2xcos2x(sin5x+cos3xsin2x+sin3xcos2x+cos5x)2dx is equal to...

Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the point P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of ∆PTQ is -...

If ∑i=19(xi - 5) = 9 and ∑i=19(xi - 5)2 = 45, then the standard deviation of the 9 items x1, x2, ....., x9 is-...

The value of ∫-π2π2sin2x1+2x dx is :...

If sum of all the solutions of the equation 8 cos x. cosπ6+x.cosπ6-x-12 = 1 in [0, π] is kπ, then k is equal to :...

Let y = y(x) be the solution of the differential equation sin x dydx + y cos x = 4x, x ∈ (0, π). If y π2 = 0, then y π6 is equal to :...

If L1 is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L2 is the line of intersection of the planes x + 2y - z - 3 =0, 3x - y + 2z - 1 = 0, then the distance of th...

If α = 3 sin-1 and β = 3 cos-1 where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)...

Let ƒ(x) = 7tan8x + 7tan6x − 3tan4x − 3tan2x for all x ∈ . Then the correct expression(s) is(are)...

Let P1 : 2x + y – z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE ?

ABCD is a trapezium such that AB and CD are parallel and BC ⏊ CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to