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

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

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In triangle A B C ,a , b , c are the lengths of its sides and A , B ,C are the angles of triangle A B Cdot The correct relation is given by (a) (b-c)sin((B-C)/2)=acosA/2 (b) (b-c)cos(A/2)=asin((B-C)/2) (c) (b+c)sin((B+C)/2)=acosA/2 (d) (b-c)cos(A/2)=2asin(B+C)/2

The incircle of DeltaABC touches side BC at D. The difference between BD and CD (R is circumradius of DeltaABC ) is (a) |4 R sin.(A)/(2)sin.(B -C)/(2)| (b) |4R cos.(A)/(2) sin.(B -C)/(2)| (c) |b-c| (d) |(b-c)/(2)|

If A+B+C=180^@ prove that: sin(B+2C)+sin(C+2A)+sin(A+2B)= 4 sin((B-C)/2)sin((C-A)/2)sin((A-B)/2)

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

If A,B,C are the angles of a triangle, show that, (i) sin B cos(C +A) + cos B sin (C +A) = 0

(vii) (b^(2) -c^(2)) cos 2A + (c^(2) -a^(2)) cos 2B + (a^(2) -b^(2)) cos 2C=0

C F is the internal bisector of angle C of A B C , then C F is equal to (a) (2a b)/(a+b)cos(C/2) (b) (a+b)/(2a b)cosC/2 (c) ( bsinA)/(sin(B+C/2)) (d) none of these

If A+B+C=180^@ then prove that sin( A/2)+sin( B/2)+sin( C/2) = 1+4 sin( (pi-A)/4)sin((pi-B)/4)sin ((pi-C)/4)

Eliminate x and y from the following equations : a sin ^(2)+ b cos^(2) x=c, b sin ^(2) y+ a cos^(2) y=d, a tan x= b tan y .

Simplify: 1 + (sin(A - B))/(cos A cosB) + (sin (B - C))/(cos B cos C) + (sin (C - A))/(cos C cos A)

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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