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Prove that a^(2) sin 2B + b^(2) sin 2A =...

Prove that `a^(2) sin 2B + b^(2) sin 2A = 4 Delta`

A

`2lamda`

B

`lamda`

C

`4lamda`

D

none of these

Text Solution

Verified by Experts

We have,
`a^(2)sin2B+b^(2)sin2A`
`=2a^(2)sinBcosB+2b^(2)sinAcosA`
`=2a^(2)sinBcosB+2(ab)sinBcosA` `[becauseasinB=bsinA]`
`=2asinB(acosB+bcosA)`
`=2acsinB` `[becauseasinB=bsinA]`
`=4lamda` `[becauselamda=1/2acsinB]`
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OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  3. The area of a regular polygon of n sides is (where r is inradius, R is...

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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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  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

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

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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 DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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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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