lim n→∞ \(\frac{1}{n^3} \)
\[\sum_{k=1}^{n} k^{2} = \]
x
\(\frac{x}{2}\)
\(\frac{x}{3}\)
\(\frac{x}{4}\)
The correct option is (C) \(\frac{x}{3}\)
If sin-1x = 2 tan-1x , then number of integral values of x is equal to:
The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
The number of electrons with (n+1) values equal to 3,4 and 5 in an element with atomic number (z) 24 are respectively (n = principal quantum number and l = azimuthal quantum number)
Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact with each other co-axially. The focal length of the combination is:
If i=√-1 then
\[Arg\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right] =\]Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation. All possible values which satisfy the given trigonometric equation are called solutions of the given trigonometric equation.
A list of trigonometric equations and their solutions are given below:
Trigonometrical equations | General Solutions |
sin θ = 0 | θ = nπ |
cos θ = 0 | θ = (nπ + π/2) |
cos θ = 0 | θ = nπ |
sin θ = 1 | θ = (2nπ + π/2) = (4n+1) π/2 |
cos θ = 1 | θ = 2nπ |
sin θ = sin α | θ = nπ + (-1)n α, where α ∈ [-π/2, π/2] |
cos θ = cos α | θ = 2nπ ± α, where α ∈ (0, π] |
tan θ = tan α | θ = nπ + α, where α ∈ (-π/2, π/2] |
sin 2θ = sin 2α | θ = nπ ± α |
cos 2θ = cos 2α | θ = nπ ± α |
tan 2θ = tan 2α | θ = nπ ± α |