Advertisements
Advertisements
Question
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
Advertisements
Solution
`cos[sin^-1 1/4 + sec^-1 4/3] = cos[sin^-1 1/4 + cos^-1 3/4]`
= `cos(sin^-1 1/4) cos(cos^-1 3/4) - sin(sin^-1 1/4) sin(cos^-1 3/4)`
= `3/4 sqrt(1 - (1/4)^2) - 1/4 sqrt(1 - (3/4)^2`
= `3/4 sqrt(15)/4 - 1/4 sqrt(7)/4`
= `(3sqrt(15) - sqrt(7))/6`
APPEARS IN
RELATED QUESTIONS
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1 - cos x)/(1 + cos x)))`, 0 < x < π
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that `tan^(-1) sqrt(x) = 1/2 cos^(-1) (1 - x)/(1 + x), x ∈ [0, 1]`.
Prove that `cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sinx))/(sqrt(1 + sin x) - sqrt(1 - sinx))) = x/2, x ∈ (0, pi/4)`.
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 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:
sin(tan–1x), |x| < 1 is equal to
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"cos"^-1 (1/2)`
`"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:
ЁЭР┤' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.
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
`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 ______.
Principal value of `"cosec"^(−1)((−2)/sqrt3)` is equal to ______.
