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If the sides a , ba n dCof A B C are in ...

If the sides `a , ba n dCof A B C` are in `AdotPdot,` prove that `2sinA/2sinC/2=sinB/2,` `acos^2C/2+cos^2A/2=(3b)/2`

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To prove the two statements given in the problem, we will follow a systematic approach. Let's break down the solution step by step. ### Given: The sides \( a, b, c \) of triangle \( ABC \) are in Arithmetic Progression (AP). ### Part 1: Prove that \[ ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. If cosA/2=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

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

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  3. If the sides a , ba n dCof A B C are in AdotPdot, prove that 2sinA/2s...

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  4. Prove that (cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2

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

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

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  7. Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

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

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

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

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

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

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  13. The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the a...

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

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

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

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  17. If A=30^0, a=7,a n db=8 in A B C , then find the number of triangles ...

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  18. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

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  19. In A B C ,s i d e sb , c and angle B are given such that a has two va...

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  20. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

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