Advertisements
Advertisements
प्रश्न
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
उत्तर
Let tan-1 x = θ
x = tan θ
sin 2θ = `(2 tan θ)/(1 + tan^2 θ) = "2x"/(1 + x^2)`
2θ = `sin^-1 ("2x"/(1 + x^2))`
∴ 2 tan-1 x = `sin^-1 ("2x"/(1 + x^2))` = RHS
APPEARS IN
संबंधित प्रश्न
Find the domain of `f(x)=cotx+cot^-1x`
Find the principal value of the following: `sin^-1 (1/2)`
Evaluate:
`cos[tan^-1 (3/4)]`
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
Which of the following functions is inverse of itself?
