Advertisements
Advertisements
Question
Select the correct option from the given alternatives :
In ∆ABC if cot A cot B cot C > 0 then the triangle is _________
Options
Acute angled
right angled
obtuse angled
isosceles right angled
Advertisements
Solution
Acute angled
Explanation:
cot A cot B cot C > 0
- Case I:
cot A, cot B, cot C > 0
∴ cot A > 0, cot B > 0, cot C > 0
∴ 0 < A < `pi/2`, 0 < B < `pi/2`, 0 < C < `pi/2`
∴ ΔABC is an acute angled triangle. - Case II:
Two of cot A, cot B, cot C < 0
0 < A, B, C < π and
two of cot A, cot B, cot C < 0
∴ Two of angles A, B, C are in 2nd quadrant which is not possible.
APPEARS IN
RELATED QUESTIONS
In ΔABC, A + B + C = π show that
sin A + sin B + sin C = `4cos "A"/2 cos "B"/2 cos "C"/2 `
In ΔABC, A + B + C = π show that
`sin^2 "A"/2 + sin^2 "B"/2 - sin^2 "C"/2 = 1 - 2cos "A"/2 cos "B"/2 sin "C"/2`
In ΔABC, A + B + C = π show that
`tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2tan "A"/2` = 1
In ΔABC, A + B + C = π show that
`cot "A"/2 + cot "B"/2 + cot "C"/2 = cot "A"/2 cot "B"/2 cot "C"/2`
In ΔABC, A + B + C = π show that
tan 2A + tan 2B + tan 2C = tan 2A tan 2B tan 2C
In ΔABC, A + B + C = π show that
cos2A +cos2B – cos2C = 1 – 2 sin A sin B cos C
Prove the following:
If sin α sin β − cos α cos β + 1 = 0 then prove cot α tan β = −1
Prove the following:
`cos (2pi)/15 cos (4pi)/15cos (8pi)/15cos (16pi)/15 = 1/16`
Prove the following:
`(1 + cos pi/8)(1 + cos (3pi)/8)(1 + cos (5pi)/8)(1 + cos (7pi)/8) = 1/8`
Prove the following:
If A + B + C = `(3pi)/2`, then cos 2A + cos 2B + cos 2C = 1 − 4 sin A sin B sin C
Prove the following:
In ∆ABC, ∠C = `(2pi)/3`, then prove that cos2A + cos2B − cos A cos B = `3/4`
If A and Bare supplementary angles, then `sin^2 "A"/2 + sin^2 "B"/2` = ______.
If `cos "A" = 3/4,`then 32 sin`"A"/2 cos (5"A")/2` = ?
`(sin20^circ +2sin40^circ)/sin70^circ=` ______.
If A + B + C = 180°, then `sum tan A/2 tan B/2` is ______.
Let A, B and C are the angles of a triangle and `tan(A/2) = 1/3, tan(B/2) = 2/3`. Then, `tan(C/2)` is equal to ______.
If A + B + C = 270°, then cos 2A + cos 2B + cos 2C is equal to ______.
In a ΔABC, if cos A cos B cos C = `(sqrt(3) - 1)/8` and sin A sin B sin C = `(3 + sqrt(3))/8`, then the angles of the triangle are ______.
ΔABC is a right angled isosceles triangle with ∠B = 90°. If D is a point on AB, ∠CDB = 15° and AD = 35 cm, then CD is equal to ______.
If sin A + sin B = C, cos A + cos B = D, then the value of sin(A + B) = ______.
If x + y + z = 180°, then cos 2x + cos 2y – cos 2z is equal to ______.
If A + B + C = π(A, B, C > 0) and the ∠C is obtuse, then ______.
If A + B + C = 270°, then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to ______.
If A, B, C are the angles of a triangle, then sin2 A + sin2 B + sin2 C – 2 cos A cos B cos C is equal to ______.
If A + B = C = 180°, then the value of `cot A/2 + cot B/2 + cot C/2` will be ______.
If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is ______.
lf A + B + C = π, then `cosA/(sinBsinC) + cosB/(sinCsinA) + cosC/(sinAsinB)` is equal to ______.
The value of cot A cot B + cot B cot C + cot C cot A is ______.
