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

(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))`

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(ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin (A-B))/(sin C)=0

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

If alpha and beta be two roots of the equation a cos theta+ b sin theta=c , show that sin alpha+ sin beta=(2bc)/(a^(2)+b^(2)) ,sin alpha sin beta =(c^(2)-a^(2))/(a^(2)+b^(2)) and tan (alpha+ beta)=(2ab)/(a^(2)-b^(2))

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

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

Factorise : (a^(2)-b^(2))(a+b)+(b^(2)-c^(2))(b+c)+(c^(2)-a^(2))(c+a)

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

If "sin"^(-1) (x)/(a)+"sin"^(-1)(y)/(b)="sin"^(-1)(c^(2))/(ab) , prove that, b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4))+a^(2)y^(2)=c^(4)

In any triangle ABC, prove that (a^(2)sin(B-C))/(sin B + sinC) + (b^(2)sin(C-A))/(sinC + sinA) +(c^(2)sin(A-B))/(sinA + sinB)=0

In any /_\ABC ,prove that sin(B-C)/(sin(B+C))=(b^2-c^2)/(a^2)

CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Short Answer Type Questions
  1. (viii) (b^(2) -c^(2)) cos 2A + (c^(2)-a^(2)) cos 2B + (a^(2)-b^(2)) co...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. In triangle ABC ,a=2,b=sqrt3 and A=90^@, then find B?

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  15. In any triangle ABC, if cosA cos B + sin A sin B sinC =1 then prove th...

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  16. In any triangle ABC, prove that cosA + cos B + cos C le 3/2

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  17. In any triangle ABC, show that (a sin C)/(b - a cosC)= tanA.

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  18. If B=30^(@), b=3sqrt(2)-sqrt(6), c=6-2sqrt(3), solve the triangle.

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  19. In any triangle ABC, if cosA + cos B + cosC =3/2, then show that the t...

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  20. If A,B,C be the angles ofa triangle then prove that (sin A + sin B)(si...

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