Advertisements
Advertisements
प्रश्न
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
विकल्प
`1/sqrt2`
`sqrt3/2`
`1/2`
`pi/4`
Advertisements
उत्तर
`cos[tan^-1 1/3 + tan^-1 1/2] = \underlinebb((1/sqrt2))`
Explanation:
Let consider, y = `cos[tan^-1 1/3 + tan^-1 1/2]`
∵ `tan^-1 a + tan^-1 b = tan^-1 ((a + b)/(1 - ab))`, if ab < 1
∴ a = `1/3`; b = `1/2`; ab = `1/6 < 1`;
y = `cos [tan^-1 ((1/3 + 1/2)/(1 - 1/3 xx 1/2))]`
Thus, y = `cos [tan^-1 (((3 + 2)/6)/((6 - 1)/6))]`
y = `cos[tan^-1 5/5]`
y = cos[tan−1(1)]
y = `cos(pi/4)`
y = cos(45°)
∴ y = `1/sqrt2`
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation has a solution or not?
cos2θ = – 1.
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
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 cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
The principal value of sin–1 `(- sqrt3/2)` is ______.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
Find the principal solutions of cosec x = 2
Find the principal solutions of tan x = `-sqrt(3)`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
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 value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The general solution of sin 2x = cos 2x is ______
The general solution of cot θ + tan θ = 2 is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
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 ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
