Advertisements
Advertisements
प्रश्न
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
उत्तर
LHS = `cot^-1 1/3 - tan^-1 1/3`
`= tan^-1 3 - tan^-1 1/3 ....[because cot^-1 "x" = tan^-1 (1/"x")]`
`= tan^-1 [(3 - 1/3)/(1 + 3(1/3))]`
`= tan^-1 [(8/3)/(1 + 1)]`
`= tan^-1 (4/3)`
`= cot^-1 (3/4) ....[tan^-1 "x" = cot^-1 (1/"x")]`
= RHS.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
tan θ = – 1
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sin 2θ = `1/2`
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
2sinθ = 3
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2𝑥 = 1
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The general solution of the equation tan θ tan 2θ = 1 is given by ______
The general solution of cot θ + tan θ = 2 is ______.
The general solution of cosec x = `-sqrt2` is ______
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
The general solution of the equation tan2 x = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
