Advertisements
Advertisements
प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Advertisements
उत्तर
We know the principle solution of a trigonometric equation lies in the interval (0, 2π).
For, sec θ = `2/(sqrt3)`,
we know sec θ is positive only in the 1st and 4th quadrant in the interval (0, 2π).
Now in the 1st quadrant,
sec θ = `2/(sqrt3) ⇒ θ = π/6`.
And, in 4th quadrant,
sec θ = `2/(sqrt3) ⇒ θ = 2π - π/6 = (11π)/6`.
Thus, the principle solution of the equation sec θ = `2/(sqrt3) "is" θ = π/6 "and" (11π)/6`.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
tan θ = – 1
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation has a solution or not?
cos2θ = – 1.
State whether the following equation has a solution or not?
2sinθ = 3
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan^2 theta = 3`
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
Find the principal solutions of sin x − 1 = 0
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`int 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
The general solution of sec θ = `sqrt2` is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The principal solutions of cot x = `sqrt3` are ______.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The general solution of cosec x = `-sqrt2` is ______
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Which of the following equation has no solution?
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of the equation tan2 x = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution of cot 4x = –1 is ______.
