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3(sinx – cosx)4 + 6(sinx + cosx)2 + 4(sin6x + cos6x) = ______.
Concept: undefined >> undefined
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
Concept: undefined >> undefined
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The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.
Concept: undefined >> undefined
State whether the statement is True or False? Also give justification.
If tanA = `(1 - cos B)/sinB`, then tan2A = tanB
Concept: undefined >> undefined
State whether the statement is True or False? Also give justification.
If cosecx = 1 + cotx then x = 2nπ, 2nπ + `pi/2`
Concept: undefined >> undefined
State whether the statement is True or False? Also give justification.
If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`
Concept: undefined >> undefined
State whether the statement is True or False? Also give justification.
If tan(π cosθ) = cot(π sinθ), then `cos(theta - pi/4) = +- 1/(2sqrt(2))`.
Concept: undefined >> undefined
In the following match each item given under the column C1 to its correct answer given under the column C2:
| Column A | Column B |
| (a) sin(x + y) sin(x – y) | (i) cos2x – sin2y |
| (b) cos (x + y) cos (x – y) | (ii) `(1 - tan theta)/(1 + tan theta)` |
| (c) `cot(pi/4 + theta)` | (iii) `(1 + tan theta)/(1 - tan theta)` |
| (d) `tan(pi/4 + theta)` | (iv) sin2x – sin2y |
Concept: undefined >> undefined
If the imaginary part of `(2z + 1)/(iz + 1)` is –2, then show that the locus of the point representing z in the argand plane is a straight line.
Concept: undefined >> undefined
Let z1 and z2 be two complex numbers such that `barz_1 + ibarz_2` = 0 and arg(z1 z2) = π. Then find arg (z1).
Concept: undefined >> undefined
Let z1 and z2 be two complex numbers such that |z1 + z2| = |z1| + |z2|. Then show that arg(z1) – arg(z2) = 0.
Concept: undefined >> undefined
If |z| = 2 and arg(z) = `pi/4`, then z = ______.
Concept: undefined >> undefined
The locus of z satisfying arg(z) = `pi/3` is ______.
Concept: undefined >> undefined
What is the polar form of the complex number (i25)3?
Concept: undefined >> undefined
The amplitude of `sin pi/5 + i(1 - cos pi/5)` is ______.
Concept: undefined >> undefined
Show that the complex number z, satisfying the condition arg`((z - 1)/(z + 1)) = pi/4` lies on a circle.
Concept: undefined >> undefined
If arg(z – 1) = arg(z + 3i), then find x – 1 : y. where z = x + iy.
Concept: undefined >> undefined
z1 and z2 are two complex numbers such that |z1| = |z2| and arg(z1) + arg(z2) = π, then show that z1 = `-barz_2`.
Concept: undefined >> undefined
If for complex numbers z1 and z2, arg (z1) – arg (z2) = 0, then show that `|z_1 - z_2| = |z_1| - |z_2|`.
Concept: undefined >> undefined
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
Concept: undefined >> undefined
