Advertisements
Advertisements
Question
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Advertisements
Solution
`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
RELATED QUESTIONS
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Prove `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
sin (tan–1 x), |x| < 1 is equal to ______.
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
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:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"tan"^-1 2 "x + tan"^-1 3 "x" = pi/4`, then x is ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
`"sin"^-1 ((-1)/2)`
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 ∠CAB = ________.
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
If \[\tan^{-1}\left(\frac{x}{2}\right)+\tan^{-1}\left(\frac{y}{2}\right)+\tan^{-1}\left(\frac{z}{2}\right)=\frac{\pi}{2}\] then xy + yz + zx =
