Advertisements
Advertisements
प्रश्न
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
विकल्प
`pi/5`
`(2pi)/5`
`(3pi)/5`
`(4pi)/5`
Advertisements
उत्तर
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is `(2pi)/5`.
Explanation:
We know tan–1x + cot–1x = `pi/2`.
Therefore cot–1x = `pi/2 - pi/10`
⇒ cot–1x = `pi/2 - pi/10 = (2pi)/5`.
APPEARS IN
संबंधित प्रश्न
Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 < x < a/sqrt3`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1+ x^2) + cos^(-1) (1-y^2)/(1+y^2)]`, |x| < 1, y > 0 and xy < 1
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Solve: tan-1 4 x + tan-1 6x `= π/(4)`.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to
Evaluate `tan^-1(sin((-pi)/2))`.
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
If 3 tan–1x + cot–1x = π, then x equals ______.
The value of the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x2 – 23x – 12 = 0
