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:
cosθ = `(1)/(2)`
Find the general solution of the following equation:
sinθ = `1/2`.
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:
sec θ = `sqrt(2)`.
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:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation have solution or not?
3 tanθ = 5
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:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
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
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
The principal value branch of sec-1x is ______.
`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
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
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 `tan^-1 1/2 = 1/3 tan^-1 11/2`
Find the principal solutions of cos 2𝑥 = 1
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The general solution of sin 2x = cos 2x is ______
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The general solution of cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
Which of the following equation has no solution?
The general solution of the equation tan2 x = 1 is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
The general solution of cot 4x = –1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
