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In DeltaABC, if b+c=3a, then prove that:...

In `DeltaABC`, if `b+c=3a`, then prove that:
`cotB/2.cotC/2=2`

A

1

B

2

C

`sqrt3`

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
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ML KHANNA-PROPERTIES OF TRIANGLES -Problem Set (3)(MULTIPLE CHOICE QUESTIONS)
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  2. In DeltaABC, if b+c=3a, then prove that: cotB/2.cotC/2=2

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  3. In Delta ABC if a= 16 , b= 24 and c = 20 then cos (B/2)

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  4. If the hypotenuse of a right-angled triangle is four times the length ...

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  5. Prove that bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2...

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  6. If the sides of a triangle a,b,c be in A.P., then a cos^2 ""C/2 +c cos...

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  7. (b-c)/a cos^2 "" 1/2 A+ (c-a)/b cos^2 "" 1/2 B+(a-b)/c cos^2 ""1/2 C=

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  8. 2 abc.cos ""A/2 cos "" B/2 ""cos""C/2=

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  9. In a triangle ABC, abc s sin "" A/2 sin ""B/2 sin "" C/2=

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  10. 1-tan""A/2.tan""B/2=

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  11. If the sides of triangle a,b,c be is A.P. then tan""A/2+tan""C/2=

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  12. If in a triangle ABC, S = a^2 - (b -c)^2 then tan A is equal to

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  13. If c^(2)=a^(2) +b^(2), then 4s(s-a)(s-b)(s-c) is equal to

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  14. If in a triangle ABC cos A cos B+sin Asin B sin C = 1, then the sides ...

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  15. If in a triangle ABC cos Acos B + sin A sin B sin C = 1, then the tria...

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  16. If in a !ABC , a = 6 , b = 3 and cos (A -B) =4/5,then its area in squa...

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  17. In a triangle ABC we define x = tan""(B-C)/2 tan""A/2, y=tan""(C-A)/2 ...

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  18. In a triangle ABC if a =5,b= 4,cos (A - B) = 31/32, then the third sid...

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  19. In a triangle cot A cot B cot C gt 0, then the triangle is

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  20. If cos B cos C+sin B sin C sin^2 A = 1, then the triangle ABC is

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