Advertisements
Advertisements
Question
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
Advertisements
Solution
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
RELATED QUESTIONS
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Find the principal value of the following:
`tan^(-1) (-sqrt3)`
Find the principal value of the following:
`sec^(-1) (2/sqrt(3))`
Find the principal value of the following:
`"cosec"^(-1)(-sqrt2)`
If sin−1 x = y, then ______.
Find the value of the following:
`cos^(-1) (cos (13pi)/6)`
`sin^-1 1/2-2sin^-1 1/sqrt2`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)=sin^-1x^2`
Prove that:
cot−1 7 + cot−1 8 + cot−1 18 = cot−1 3 .
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
Find the principal value of the following: tan-1(– 1)
Find the principal value of the following: cos- 1`(-1/2)`
Evaluate the following:
`cos^-1(1/2) + 2sin^-1(1/2)`
Prove the following:
`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Find the principal value of `tan^-1 (sqrt(3))`
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
The domain of y = cos–1(x2 – 4) is ______.
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
When `"x" = "x"/2`, then tan x is ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
The range of sin-1 x + cos-1 x + tan-1 x is ____________.
3 tan-1 a is equal to ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
Domain and Rariges of cos–1 is:-
Find the principal value of `tan^-1 (sqrt(3))`
Values of tan–1 – sec–1(–2) is equal to
What is the values of `cos^-1 (cos (7pi)/6)`
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
If f'(x) = x–1, then find f(x)
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
