Advertisements
Advertisements
प्रश्न
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
विकल्प
θ = `(2npi)/(p +- q)`
θ = 2nπ
θ = 2nπ ± p
θ = 2nπ ± q
Advertisements
उत्तर
If cos pθ = cos qθ, p ≠ q, then, θ = `bb(underline((2npi)/(p +- q))`
Explanation:
Given, cos pθ = cos qθ
cos pθ – cos qθ = 0
`2sin((pθ + qθ)/2) sin((pθ - qθ)/2)` = 0 ...(cos C – cos D)
`sin((pθ + qθ)/2)` = 0 or `sin ((pθ - qθ)/2)` = 0
`(pθ + qθ)/2` = nπ or `(pθ - qθ)/2` = nπ
θ = `(2nπ)/((p + q))` or `(2nπ)/((p - q))` = θ
∴ θ = `(2nπ)/(p +- q)`
संबंधित प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
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:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
sin θ = tan θ
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
The principal value branch of sec-1x is ______.
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x − 1 = 0
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
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
`int (sin (log x))^2/x` log x dx = ?
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The value of sin 18° is ______.
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
Find the principal solutions of cot θ = 0
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
If tan3θ = cotθ, then θ =
