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(vi) (a^(2)-b^(2) -c^(2))tan A + (a^(2)...

(vi) `(a^(2)-b^(2) -c^(2))tan A + (a^(2) - b^(2) +c^(2))tan B=0`

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(vii) (b^(2) +c^(2) -a^(2)) tan A = (a^(2) -b^(2) +c^(2))tan B

Prove that for a triangle ABC, (a^2-b^2-c^2) tan A+(a^2-b^2+c^2)tan B=0

If (b^(2) + c^(2) - a^(2))/(2bc), (c^(2) + a^(2) - b^(2))/(2ca), (a^(2) + b^(2) - c^(2))/(2ab) are in A.P. and a+b+c = 0 then prove that a(b+c-a), b(c+a-b), c(a+b-c) are in A.P.

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

If (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .

If a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

If a tan x+ b tan y+ c tan z=m , then show that the minimum value of tan^(2)x+tan^(2)y+tan^(2)z "is" (m^(2))/(a^(2)+b^(2)+c^(2)) .

If (a^(2)-b^(2))sin theta+2 ab cos theta-(a^(2)+b^(2))=0 , then prove that tan theta=(1)/(2)((a)/(b)-(b)/(a)) .

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

If (a + b) tan (theta - phi) = (a-b) tan (theta + phi) " and " a cos 2 phi + b cos 2 theta = c, "show that" a^(2) -b^(2) + c^(2) = 2a cos 2 phi

CHHAYA PUBLICATION-PROPERTIES OF TRIANGLE -Very Short Answer Type Questions
  1. In a triangle the sides are in the ratio sqrt(2) :2 : (sqrt(3)+1). Fin...

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  2. If the angles of a triangle are in the ratio 2:3:7 and the circumradiu...

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  3. In triangleABC angleB=60^(@), c=2sqrt(3), b =3sqrt(2) then find angle...

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  4. In a triangle ABC the angle A=60^(@) and b:c = (sqrt(3)+1):2. Find the...

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  5. If the two sides and the included angle are respectively a=sqrt(3)+1, ...

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  6. Find the angles of the triangle whose sides are (sqrt(3)+1)/(2sqrt(2))...

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  7. Find the area of the triangle if (i) a=13, b=14, c=15 (ii) a:b :c ...

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  8. If in a triangle ABC, a=3, b=5 and c=7, show that the triangle is obtu...

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  9. If (sin A)/3 = (sin B)/3 = (sin C)/4, then prove that, cos C=1/9.

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  10. If in a triangle ABC, (a-b+c)/2 = ab/(b+c-a) then prove that angleC=90...

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  11. If a=3, b=4, c=5, find the value of tan( B/2).

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  12. If a=2b and A=3B, find the angles of the triangle ABC.

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  13. (i) (b+c) cos A + (c+a) cosB + (a+b) cos C= a+b+c

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  14. (ii) (b-c) sin A + (c-a) sinB+ (a-b) sinC=0

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  15. (iii) a(b cosC - c cosB) = b^(2) -c^(2)

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  16. (iv) a^(2)(cos^(2) B - cos^(2)C) + b^(2) (cos^(2) C- cos^(2)A) + c^(2)...

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  17. (v) 2(bc cosA + ca cosB + ab cosC) = a^(2) +b^(2)+c^(2)

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  18. (vi) (a^(2)-b^(2) -c^(2))tan A + (a^(2) - b^(2) +c^(2))tan B=0

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  19. (vii) (b^(2) +c^(2) -a^(2)) tan A = (a^(2) -b^(2) +c^(2))tan B

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  20. (viii) (b+c-a) tan( A/2) = (c+a-b) tan( B/2) = (a+b-c) tan C/2

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