Advertisements
Advertisements
प्रश्न
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Advertisements
उत्तर
`tan^-1 sqrt(3) - sec^-1(-2) = tan^-1 sqrt(3) - [pi - sec^-1 2]`
= `pi/3 - pi + cos^-1(1/2)`
= `- (2pi)/3 + pi/3`
= `- pi/3`.
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) `
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Prove the following:
3 sin−1 x = sin−1 (3x − 4x3), `x ∈ [-1/2, 1/2]`
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
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:
`tan^(-1) 63/16 = sin^(-1) 5/13 + cos^(-1) 3/5`
Find: ∫ sin x · log cos x dx
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Choose the correct alternative:
If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to
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:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
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?
The value of the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
The value of sin (2tan-1 (0.75)) is equal to ____________.
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50
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 Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
