Advertisements
Advertisements
प्रश्न
sin (tan–1 x), |x| < 1 is equal to ______.
विकल्प
`x/(sqrt(1-x^2))`
`1/sqrt(1-x^2)`
`1/sqrt(1+x^2)`
`x/(sqrt(1+ x^2))`
Advertisements
उत्तर
sin (tan–1 x), |x| < 1 is equal to `bbunderline (x/(sqrt(1+ x^2)))`.
Explanation:
Let tan–1 x = θ
= x = tan θ, where `θ ∈ (- pi/2, pi/2)`
∴ sin (tan–1 x) = sin θ
Now, sin θ = `1/("cosec" θ)`
= `1/sqrt(1+cot^2θ)`
= `1/sqrt(1+ 1/tan^2θ)`
= `x/(sqrt(x^2 + 1)`
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:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π
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`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
if `tan^(-1) (x-1)/(x - 2) + tan^(-1) (x + 1)/(x + 2) = pi/4` then find the value of x.
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
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`
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 `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
If cos–1x > sin–1x, then ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"tan"^-1 (sqrt3)`
`"cos"^-1 (1/2)`
`"sin"^-1 ((-1)/2)`
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Measure of ∠DAB = ________.
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Domain and Range of tan-1 x = ________.
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
Find the value of `sin^-1 [sin((13π)/7)]`
The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
Solve:
sin–1 (x) + sin–1 (1 – x) = cos–1 x
