30 Questions
What is the general form of a trigonometric equation that can be reduced to a rational equation with respect to the arguments sin x, cos x, tan x, and cot x?
R(sin kx, cos nx, tan mx, cot lx) = 0
What is the formula for cos x in terms of tan x?
cos x = 1 / (1 + tan^2 x)
What is the purpose of the DYGU formulae in trigonometry?
To reduce trigonometric equations to rational equations with respect to the arguments sin x, cos x, tan x, and cot x
What is the substitution used to reduce the trigonometric equation to a rational equation with respect to x?
t = tan x
What is the general solution to the equation (cos x - sin x)(2 tan x + 1) + 2 = 0?
x = 2nπ ± π/3
What is a trigonometric equation?
An equation involving one or more trigonometric ratios of an unknown angle
What is a root of a trigonometric equation?
The value of the unknown angle that satisfies the equation
What is the main difference between a trigonometric equation and a trigonometric identity?
A trigonometric equation is satisfied for some particular values of the unknown angle, while a trigonometric identity is true for every value of the unknown angle
What is a particular solution of a trigonometric equation?
A specific value of the unknown angle that satisfies the equation
What is the value of sin x cos x in terms of t, where sin x + cos x = t?
1/2(t2 - 1)
Why do trigonometric equations generally have more than one solution?
Because trigonometric ratios are periodic in nature
What is the solution to the equation tan x = 2 in the form x = nπ ±...?
nπ ± π/3
What is the equation (t2 + 1)(1 - t2) = 0 equivalent to?
tan x = 2 and tan x = -2
What is the form of the equation R(sin x + cos x, sin x cos x) = 0, where R is a rational function?
A polynomial equation in sin x and cos x
What is the value of x that satisfies the equation tan x = 2, where x is in the form x = nπ ±...?
nπ ± π/3
What can be concluded about the trigonometric equation |secθ + tanθ| = 2?
It has a particular solution θ = 60°.
Which of the following statements is true about the trigonometric identity cos²x = 1 - sin²x?
It is true for every value of x in the domain of the function.
What is the difference between a trigonometric equation and a trigonometric identity?
A trigonometric equation is satisfied for some particular values of the unknown angle, while a trigonometric identity is true for every value of the unknown angle.
What is the name of the value of the unknown angle that satisfies the given trigonometric equation?
Root of the equation
What is the characteristic of trigonometric ratios that results in trigonometric equations having more than one solution?
Periodicity
If sin x + cos x = t, then what is the value of sin x cos x in terms of t?
(t2 - 1)/2
What is the general form of the trigonometric equation that can be reduced to a rational equation with respect to the arguments sin x, cos x, tan x, and cot x?
R(sin x + cos x, sin x cos x) = 0
If tan x = 2, then what is the value of x in the form x = nπ ±...?
x = nπ ± π/6
What is the equivalent form of the equation (t2 + 1)(1 - t2) = 0, where t = sin x + cos x?
tan x = 2 or tan x = -2
What is the value of x that satisfies the equation tan x = 2, where x is in the form x = nπ ±...?
x = nπ ± π/6
If t = tan(x/2), then what is the value of sin(x) in terms of t?
2t/(1 + t^2)
What is the value of cos(x) in terms of t, where t = tan(x) and x is in the first quadrant?
1/(t^2 + 1)
If sin(x) + cos(x) = t, then what is the value of sin(x)cos(x) in terms of t?
(t^2 - 1)/2
What is the general solution to the equation (cos(x) - sin(x))(2 tan(x) + 1) + 2 = 0?
x = nπ ± π/3
If R(sin(x), cos(x), tan(x), cot(x)) = 0 is a trigonometric equation, what is the form of the equation after reducing it to a rational equation with respect to x?
R(t, 1/t, t^2, 1/t^2) = 0
Learn about trigonometrical equations and inequations, including their definitions, examples, and differences from trigonometric identities. Understand how to solve these equations and inequations with ease.
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