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If Delta denotes the area of DeltaABC, t...

If `Delta` denotes the area of `DeltaABC`, then `b^(2) sin 2C + c^(2) sin 2B` is equal to

A

`Delta`

B

`2Delta`

C

`3Delta`

D

`4Delta`

Text Solution

Verified by Experts

We have,
`R=a/(2sinA)=b/(2sinB)=c/(2sinC)`
`rArrsinB=b/(2R)` and `sinC=c/(2R)` ..(i)
`thereforeb^(2)sin2C+c^(2)sin2B`
`=2b^(2)sinCcosC+2c^(2)sinBcosB`
`=(2b^(2)c)/(2R)cosC+(2c^(2)b)/(2R)cosB` [Using(i)]
`=(bc)/R(bcosC+ccosB)=(abc)/R=4Delta`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  3. The area of the reactangle polygen of n sides is (where R is the radiu...

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  4. If the angles of a rectangle are 30^(@) and 45^(@) and the included si...

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  6. If A is the area and 2s the sum of the sides of a triangle,then

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  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

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  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  11. In a DeltaABC, AD is the altitude from A. Given bgtc ,angleC=23^(@) an...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , B and C of triangle A B C be in AdotPdot and let b ...

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