Advertisements
Advertisements
प्रश्न
If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x2 – 23x – 12 = 0
Advertisements
उत्तर
`tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)`
`\implies tan^-1 {((x - 1)/(x + 1) + (2x - 1)/(2x + 1))/(1 - ((x - 1)/(x + 1))((2x - 1)/(2x + 1)))} = tan^-1 (23/36)`
`\implies tan^-1 ((2x^2 - x - 1 + 2x^2 + x - 1)/(2x^2 + 3x + 1 - 2x^2 + 3x - 1)) = tan^-1 (23/36)` ...`{{:("Using formula:"),(tan^-1"a" + tan^-1"b" = tan^-1(("a" + "b")/(1 - "ab"))):}}`
`\implies tan^-1 ((4x^2 - 2)/(6x)) = 23/36`
∴ `(4x^2 - 2)/(6x) = 23/36`
`\implies` 6(4x2 – 2) = 23x
`\implies` 24x2 – 23x – 12 = 0
APPEARS IN
संबंधित प्रश्न
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1 - cos x)/(1 + cos x)))`, 0 < x < π
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt(3) < x < a/sqrt(3)`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Prove that `cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`.
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
If cos-1 x + cos -1 y + cos -1 z = π , prove that x2 + y2 + z2 + 2xyz = 1.
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Choose the correct alternative:
If |x| ≤ 1, then `2tan^-1x - sin^-1 (2x)/(1 + x^2)` is equal to
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
If a1, a2, a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression.
`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`
If 3 tan–1x + cot–1x = π, then x equals ______.
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
sin (tan−1 x), where |x| < 1, is equal to:
Simplest form of `tan^-1 ((sqrt(1 + cos "x") + sqrt(1 - cos "x"))/(sqrt(1 + cos "x") - sqrt(1 - cos "x")))`, `π < "x" < (3π)/2` is:
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"sin"^-1 (1/sqrt2)`
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
Solve:
sin–1 (x) + sin–1 (1 – x) = cos–1 x
