Advertisements
Advertisements
प्रश्न
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Advertisements
उत्तर
LHS = `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2`
`= cos^-1 (cos pi/6) + 2sin^-1 (sin pi/3) .....[because cos pi/6 = sqrt3/2 = sin pi/3]`
`= pi/6 + 2(pi/3) .....[because sin^-1 (sin "x") = "x", cos^-1 (cos x) = "x"]`
`= pi/6 + (2pi)/3`
`= (5 pi)/6` = RHS.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
tan θ = – 1
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation have solution or not?
cos 2θ = – 1
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
`"cos"^-1 ("cos" (7pi)/6)` = _________.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
Find the principal solutions of cosec x = 2
Find the principal solutions of tan x = `-sqrt(3)`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
The general solution of sec θ = `sqrt2` is
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
Which of the following equations has no solution?
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cosec x = `-sqrt2` is ______
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
Which of the following equation has no solution?
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of cot 4x = –1 is ______.
If tan3θ = cotθ, then θ =
