Advertisements
Advertisements
Question
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
Options
–4
0
–1
4
Solution
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to 0.
Explanation:
`"cosec" [sin^-1(-1/2)] - sec [cos^-1((-1)/2)]`
= `"cosec" [-sin^-1(1/2)] - sec [π - cos^-1((-1)/2)]`
= `"cosec" [- π/6] - sec [π - π/3]`
= `-"cosec" [π/6] - sec [(2π)/3]`
= – cosec 30° – sec 120°
= – cosec 30° – sec [(90° + 30°)]
= – 2 – [– cosec 30°]
= – 2 + cosec 30°
= – 2 + 2
= 0
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
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
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) ((1-x)/(1+x)) , x in [0, 1]`
sin (tan–1 x), | x| < 1 is equal to ______.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
Find the value of the expression in terms of x, with the help of a reference triangle
sin (cos–1(1 – x))
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`
Choose the correct alternative:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
The maximum value of sinx + cosx is ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
`"sin"^-1 (1/sqrt2)`
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
`tan(2tan^-1 1/5 + sec^-1 sqrt(5)/2 + 2tan^-1 1/8)` is equal to ______.
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
