Advertisements
Advertisements
Question
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Advertisements
Solution
L.H.S. = 2(bc cosA + ac cosB + ab cosC)
= 2bc cosA + 2ac cosB + 2ab cosC
`= 2bc((b^2 + c^2 - a^2)/(2bc)) + 2ac((c^2 + a^2 - b^2)/(2ca)) + 2ab((a^2 + b^2 - c^2)/(2ab))` ...[By cosine rule]
= b2 + c2 – a2 + c2 + a2 – b2 + a2 + b2 – c2
= a2 + b2 + c2
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
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:
cosec θ = - √2.
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
sin θ = tan θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation has a solution or not?
2sinθ = 3
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
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 = _______
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
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) =` _____
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
State whether the following equation has a solution or not?
3 sin θ = 5
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
If x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2ЁЭСе = 1
Find the principal solutions of tan x = `-sqrt(3)`
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of cot θ + tan θ = 2 is ______.
The general solution of cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
Which of the following equation has no solution?
The number of principal solutions of tan 2θ = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
