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In DeltaABC, a=x^(2)-1, b=2x+1, angleC=1...

In `DeltaABC, a=x^(2)-1, b=2x+1, angleC=120^(@)`, find c.

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AI Generated Solution

To find the length of side \( c \) in triangle \( ABC \) where \( a = x^2 - 1 \), \( b = 2x + 1 \), and \( \angle C = 120^\circ \), we can use the Law of Cosines. The Law of Cosines states that: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] ### Step-by-Step Solution: ...
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3N
  1. In DeltaABC, a:b:c=15:7:13, find cosA.

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  2. In DeltaABC, if the sides are 7, 4sqrt(3) and sqrt(13) cm, prove tha...

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  3. In DeltaABC, a=x^(2)-1, b=2x+1, angleC=120^(@), find c.

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  4. With usual notations, if in a triangle A B C(b+c)/(11)=(c+a)/(12)=(a+b...

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  5. In DeltaABC, prove that: a(cosB+cosC)=2(b+c)sin^(2)A/2.

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  6. In DeltaABC, prove that: b(cosA-cosC)=2(c-a)cos^(2)B/2

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  7. i) In DeltaABC, prove that: (b-a)/(b+a)=tanC/2. tan(B-A)/(2) ii) In ...

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  8. In DeltaABC, prove that: a/(b+c)=(1-tanB/2tanC/2)/(1+tanB/2tanC/2)

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  9. In DeltaABC, prove that: a^(2)sin2B+b^(2)sin2A=2 ab sinC

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  10. Prove that, (asin(B-C))/(b^(2)-c^(2)) = (bsin(C-A))/(c^(2)-a^(2)) = ...

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  11. In any DeltaABC, prove that ac""cosB-bc""cosA=a^(2)-b^(2)

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  12. In any triangle A B C , prove that following: \ (a^2"sin"(B-C))/(sin A...

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  13. In DeltaABC, prove that: (1+cosA.cos(B-C))/(1+cosC.cos(A-B))=(b^(2)+c...

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  14. In DeltaABC, (b^(2)+c^(2))sin(B-C)=(b^(2)-c^(2))sin(B+C), then prove t...

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  15. In a A B C , if cosC=(sinA)/(2sinB) , prove that the triangle is isos...

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  16. In triangleABC, cosA=sinB-cosC,prove that DeltaABC, is right angled.

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  17. If (sinA)/(sinC)=(sin(A-B))/(sin(B-C)), prove that a^(2), b^(2), c^(2)...

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  18. In a triangle ABC, prove that for any angle theta, b cos (A - theta) +...

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  19. In DeltaABC, 1/a,1/b,1/c are in A.P. prove that "cosec"^(2)A/2, "cosec...

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  20. If a=5, b=12 and c=13, find tanA.

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