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In a DeltaABC ,which one of the followin...

In a `DeltaABC` ,which one of the following is true?

A

`(b+c)cosA/2=asin((B+C)/2)`

B

`(b+c)cos((B+C)/2)=asinA/2`

C

`(b-c)cos((B-C)/2)=acosA/2`

D

`(b-c)cosA/2=asin((B-C)/2)`

Text Solution

Verified by Experts

We have,
`(b-c)/a=(k(sinB-sinC))/(ksinA)`
`rArr(b-c)/a=(sinB-sinC)/(sinA)=(2sin(B-C)/2cos(B+C)/2))/(2sinA/2cosA/2)`
`rArr(b-c)/a=(sin((B-C)/2))/(cosA/2)rArr(b-c)cosA/2=asin((B-C)/2)`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. In a DeltaABC,(a+c)/(a-c)tanB/2 is equal to

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  2. In a DeltaABC ,which one of the following is true?

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  3. In a DeltaABC ,a cos^(2)B/2+bcos^(2)A/2 is equal to

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  4. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

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  5. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

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

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  7. In a DeltaABC , if tanA/2=5/6 , and tanB/2=20/37, then

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  8. In DeltaABC ,if A:B:C =3:5:4,then a+b+sqrt2c=

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  9. If the lengths of the sides of a triangle are a - b , a + b and sqrt(3...

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  10. If the angles of the triangle are in A.P. and 3a^(2)=2b^(2), then angl...

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  11. In a DeltaABC ,a =5 , b= 4 , and tanC/2=sqrt(7/9), then c =

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  12. If in a !ABC sin A =4/5 and sin B =12/13, then sin C =

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

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  14. The perimeter of a !ABC is 6 times arithmetic mean of the sines of it...

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  15. If in a !ABC , a =2b ,and abs(A-B)=(pi)/3 then C =

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  16. If in a !ABC , sin A, sin B and sin C are in A.P, then

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  17. If in a !ABC , the altitudes from the vertices A , B , C on the opposi...

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  18. In a triangle ABC cos A = 7/8 , cos B = 11/16.then , cos C is equal to

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  19. If the angles A , B , C are the solutions of the equations tan^(3)-3kt...

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  20. If the angles of the triangle are in the ratio 4:1:1 , then the ratio ...

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