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Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c)...

Prove that `((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A`

A

`cos 2A`

B

`1+cos A`

C

`1-cos A`

D

`sin^2 A`

Text Solution

Verified by Experts

The correct Answer is:
D
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ML KHANNA-PROPERTIES OF TRIANGLES -Problem Set (2)(MULTIPLE CHOICE QUESTIONS)
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  2. If D id the mid-point of the side BC of a triangle ABC and AD is perpe...

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  3. Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

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  4. Let 'l' is the length of median from the vertex A to the side BC of a ...

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  5. If a triangle ABC, D is the mid point of side BC and angleADB =theta "...

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  6. The straight roads intersect at an angle of 60°. A bus on one road is ...

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  7. If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in ...

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  8. If the anngle A,B,C of a Delta ABC are in A.P then :-

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  9. If in a triangles a cos^(2)(C/2)+c cos^(2)(A/2)=(3b)/2, then the sides...

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  10. In any DeltaABC, prove that (a-b)^(2)cos^(2)""C/2+(a+b)^(2)sin^(2)""C/...

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  11. If cos A+cos B+2cos C=2 then the sides of the A B C are in A.P. (b) G...

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  12. In a triangle ABC with fixed base BC, the vertex A moves such that cos...

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  13. If in a triangle ABC, 2 (cos A)/(a)+(cos B)/(b)+2(cos C)/c=(a)/(bc)+b/...

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  14. In Delta ABC, (a + b+ c) (b + c -a) = kbc if

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  15. In a triangle ABC, 2ac sin((A-B+C)/2) =

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  16. In a A B C , prove that: (b^2-c^2)cotA+(c^2-a^2)cot B+(a^2-b^2)cotC=0

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  17. In any DeltaABC, prove that ((b^(2)-c^(2)))/a^(2)"sin 2a"+((c^(2)-a^(2...

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  18. The sides of a triangle ABC are 6 , 7 , 8 and the smallest angle being...

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  19. The sides of a triangle ABC are 6, 7, 8, the smallest angle being C th...

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  20. The sides of a triangle ABC are 6, 7, 8, the smallest angle being C th...

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