Advertisements
Advertisements
प्रश्न
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
Advertisements
उत्तर
cos A = sin B - cos C
∴ cos A + cos C = sin B
∴ `2 cos (("A + C")/2). cos (("A - C")/2)` = sin B
∴ `2 cos (pi/2 - "B"/2). "cos" (("A - C")/2)` = sin B .....[∵ A + B + C = π]
∴ `2 sin "B"/2. cos (("A - C")/2) = 2 sin "B"/2. "cos" "B"/2`
∴ `cos (("A - C")/2) = cos "B"/2`
∴ `("A - C")/2 = "B"/2`
∴ A - C = B
∴ A = B + C
∴ A + B + C = 180° gives
∴ A + A = 180°
∴ 2A = 180°
∴ A = 90°
∴ Δ ABC is a right angled triangle.
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 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:
cosec θ = - √2.
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
4sin2θ = 1.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
`tan^2 theta = 3`
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 tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x = `-1/2`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int 1/(sin x * cos x)` dx = ?
`int (sin (log x))^2/x` log x dx = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The principal solutions of cot x = `sqrt3` are ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of sin 2x = cos 2x is ______
The general solution of cot θ + tan θ = 2 is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
