Advertisements
Advertisements
प्रश्न
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
उत्तर
L.H.S. `cot(pi/4 - 2cot^-1 3)`
= `cot[tan^-1(1) - 2 tan^-1 1/3]` ......`[because cot^-1x = tan^-1 1/x]`
= `cot[tan^-1(1) - tan^-1 (2 xx 1/3)/(1 - (1/3)^2)]` ......`[because 2tan^-1x = tan^-1 (2x)/(1 - x^2)]`
= `cot[tan^-1(1) - tan^-1 (2/3)/(8/9)]`
= `cot[tan^-1(1) - tan^-1 3/4]`
= `cot[tan^-1 ((1 - 3/4)/(1 + 1 xx 3/4))]`
= `cot[tan^-1 ((1/4)/(7/4))]`
= `cot[tan^-1 1/7]` ......`[because tan^-1 1/x = cot^-1x]`
= `cot[cot^-1 (7)]`
= 7 R.H.S
Hence Proved.
APPEARS IN
संबंधित प्रश्न
Show that:
`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`
Find the principal value of `cos^(-1) (sqrt3/2)`
Find the principal value of `cos^(-1) (-1/2)`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the value of the following:
If sin−1 x = y, then
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: cos- 1`(-1/2)`
`tan^-1(tan (7pi)/6)` = ______
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
Find the principal value of the following:
cosec-1 (2)
Which of the following function has period 2?
The value of cot (- 1110°) is equal to ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
If tan-1 3 + tan-1 x = tan-1 8, then x = ____________.
`"sin"^-1 (-1/2)`
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is
`sin(tan^-1x), |x| < 1` is equal to
what is the value of `cos^-1 (cos (13pi)/6)`
Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
