Advertisements
Advertisements
प्रश्न
Solve `cos^(-1)(sin cos^(-1)x) = pi/2`
उत्तर
`sin(cos^(-1)x) = cos pi/6`
`sin(cos^(-1)x) = sqrt3/2`
`sin(cos^(-1) x) = sin pi/3`
`cos^(-1) x = pi/3`
`x = cos pi/3`
`x = 1/2`
APPEARS IN
संबंधित प्रश्न
Find : ` d/dx cos^−1 ((x−x^(−1))/(x+x^(−1)))`
Find the derivative of the following function f(x) w.r.t. x, at x = 1 :
`f(x)=cos^-1[sin sqrt((1+x)/2)]+x^x`
if `y = sin^(-1)[(6x-4sqrt(1-4x^2))/5]` Find `dy/dx `.
If `y=tan^(−1) ((sqrt(1+x^2)+sqrt(1−x^2))/(sqrt(1+x^2)−sqrt(1−x^2)))` , x2≤1, then find dy/dx.
Find `dy/dx` in the following:
`y = tan^(-1) ((3x -x^3)/(1 - 3x^2)), - 1/sqrt3 < x < 1/sqrt3`
Find `dy/dx` in the following:
`y = sin^(-1) ((1-x^2)/(1+x^2)), 0 < x < 1`
Find `dy/dx` in the following:
`y = sin^(-1)(2xsqrt(1-x^2)), -1/sqrt2 < x < 1/sqrt2`
Differentiate w.r.t. x the function:
`cot^(-1) [(sqrt(1+sinx) + sqrt(1-sinx))/(sqrt(1+sinx) - sqrt(1-sinx))]`, ` 0 < x < pi/2`
Differentiate w.r.t. x the function:
`(sin x - cos x)^(sin x - cos x), pi/4 < x < (3pi)/4`
If `xsqrt(1+y) + y sqrt(1+x) = 0`, for, −1 < x <1, prove that `dy/dx = 1/(1+ x)^2`
if `x = tan(1/a log y)`, prove that `(1+x^2) (d^2y)/(dx^2) + (2x + a) (dy)/(dx) = 0`
Find \[\frac{dy}{dx}\] at \[t = \frac{2\pi}{3}\] when x = 10 (t – sin t) and y = 12 (1 – cos t).
If y = cos (sin x), show that: `("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
If `log (x^2 + y^2) = 2 tan^-1 (y/x)`, show that `(dy)/(dx) = (x + y)/(x - y)`
If y = `(sin^-1 x)^2,` prove that `(1-x^2) (d^2y)/dx^2 - x dy/dx -2 = 0.`
The function f(x) = cot x is discontinuous on the set ______.
Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.
`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.
`lim_("x"-> 0) ("cosec x - cot x")/"x"` is equal to ____________.
If `"y = sin"^-1 ((sqrt"x" - 1)/(sqrt"x" + 1)) + "sec"^-1 ((sqrt"x" + 1)/(sqrt"x" - 1)), "x" > 0, "then" "dy"/"dx"` is ____________.
If y `= "cos"^2 ((3"x")/2) - "sin"^2 ((3"x")/2), "then" ("d"^2"y")/("dx"^2)` is ____________.
The derivative of sin x with respect to log x is ____________.
The derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `cos^-1 [(1 - x^2)/(1 + x^2)]` is equal to
Let f(x) = `cos(2tan^-1sin(cot^-1sqrt((1 - x)/x))), 0 < x < 1`. Then ______.
Differentiate `sec^-1 (1/sqrt(1 - x^2))` w.r.t. `sin^-1 (2xsqrt(1 - x^2))`.