Advertisements
Advertisements
प्रश्न
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Advertisements
उत्तर
To prove: `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
L.H.S =` tan^(-1) 2/11 + tan^(-1) 7/24`
`= tan^(-1) (2/11 + 7/24)/(1-2/11. 7/24)` `[tan^(-1) x + tan^(-1) y = tan^(-1) (x + y)/(1 - xy)]`
= tan^(-1) `((48+77)/(11xx24))/((11xx24 - 14)/(11xx24))`
`= tan^(-1) (48 + 77)/(264 - 14) = tan^(-1) 125/250 = tan^(-1) 1/2 =` R.H.S
APPEARS IN
संबंधित प्रश्न
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`
If `tan^-1(2x)+tan^-1(3x)=pi/4`, then find the value of ‘x’.
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Prove that
\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
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:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate tan (tan–1(– 4)).
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
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 cos–1x > sin–1x, then ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
If `"tan"^-1 2 "x + tan"^-1 3 "x" = pi/4`, then x is ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
