Please select a subject first
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If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
Concept: undefined >> undefined
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
Concept: undefined >> undefined
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If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
Concept: undefined >> undefined
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
Concept: undefined >> undefined
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.
Concept: undefined >> undefined
If sinx + cosx = a, then sin6x + cos6x = ______.
Concept: undefined >> undefined
If sinx + cosx = a, then |sinx – cosx| = ______.
Concept: undefined >> undefined
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
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
