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Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC...

Prove that `(b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot`

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`(b + c) cos A + (c + a) cos B + (a + b) cos C`
`= (b cos A + a cos B) + (c cos A + a cos C) + (b cos C + c cos B) = c + b + a = 2s`
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CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Prove that a(bcosC-c cosB)=b^2-c^2

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  2. If in a triangle acos^2(C/2)+ c cos^2(A/2)=(3b)/2, then find the rela...

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  3. Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

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  4. If cos(A/2)=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

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  5. If the cotangents of half the angles of a triangle are in A.P., then ...

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  6. If A, B and C are interior angles of a triangle ABC, then show that si...

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  7. In A B C ,(cot (A/2)+cot(B/2))(asin^2(B/2)+bsin^2(A/2))= (a) cotC (...

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  8. Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

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

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  10. For any triangle ABC, ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)is equa...

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  11. If the sides of a triangle are 17 , 25a n d28 , then find the greatest...

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  12. In equilateral triangle ABC with interior point D, if the perpendicula...

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  13. If area of a triangle is 2 sq. units, then find the value of the pr...

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  14. A triangle has sides 6,7, and 8. The line through its incenter para...

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  15. Each side of triangle ABC is divided into three equal parts. Find the ...

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  16. The two adjacent sides of a cyclic quadrilateral are 2and 5 and the an...

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  17. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

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  18. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

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  19. If b=3,c=4,a n dB=pi/3, then find the number of triangles that can be ...

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  20. If A=30^0, a=7,and b=8 in A B C , then find the number of triangles t...

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