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(iii) a cosA + b cos B + c cos C = 4R si...

(iii) `a cosA + b cos B + c cos C = 4R sin A sin B sinC`

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CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Short Answer Type Questions
  1. In triangle ABC, (i) asin(A/2 + B) = (b+c) sin A/2

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  2. (ii) (b-c) cos( A/2) = a sin ((B-C)/2)

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  3. (iii) a cosA + b cos B + c cos C = 4R sin A sin B sinC

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  4. (iv) a sin (B-C) + b sin(C-A) + c sin (A-B)=0

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  5. (v) (b^(2)-c^(2))/(cos B + cos C) + (c^(2)-a^(2))/( cos C + cosA) + (a...

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  6. (vi) a cos B cos C + b cos C cosA + c cosA cos B=(abc)/(4R^(2))

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  7. (vii) (b^(2) -c^(2)) cos 2A + (c^(2) -a^(2)) cos 2B + (a^(2) -b^(2)) c...

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  8. (viii) (b^(2) -c^(2)) cos 2A + (c^(2)-a^(2)) cos 2B + (a^(2)-b^(2)) co...

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  9. (ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin...

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  10. (x) (a sin(B-C))/(b^(2)-c^(2)) = (b sin (C-A))/(c^(2)-a^(2)) = (c sin(...

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  11. (xi) a^(2) sin 2B + b^(2) sin 2A = 4Delta

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  12. (xii) (b+c-a)(cot 'B/2' + cot 'C/2') = 2a cot 'A/2

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  13. (xiii) a^(3) sin (B-C) + b^(3) sin (C-A) + c^(3) sin(A-B)=0

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  14. (xiv) a cos A + b cos B + c cos C = (abc)/(2R^(2))

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  15. (xv) a cos (B-C) + b cos (C-A) + c cos (A-B) = (4(Delta))/R

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  16. If C=60^(@), show that, 2a-b = 2 c cosB

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  17. If b+c=2a, show that, 2sin 'A/2' = sin (B+A/2)

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  18. If a cos^(2)'C/2' + c cos^(2)'A/2' = (3b)/2 then show that the sides o...

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  19. In any triangle ABC, if 1/(a+c) + 1/(b+c) = 3/(a+b+c) then show that, ...

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  20. If 2 cos A = (sin B)/(sin C) then show that the triangle is isosceles.

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