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In DeltaABC, prove that: acosA+bcosB=(c)...

In `DeltaABC`, prove that: `acosA+bcosB=(c)cos(A-B)`

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To prove that in triangle \( \Delta ABC \), \( a \cos A + b \cos B = c \cos(A - B) \), we will follow a step-by-step approach. ### Step 1: Use the Law of Sines According to the Law of Sines, we have: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = k \] where \( k \) is a constant. ...
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3N
  1. In DeltaABC, prove that: sinB+sinC gt sinA

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  2. In any DeltaABC, prove that (sinA)/(sin(A+B))=a/c

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  3. In DeltaABC, prove that: acosA+bcosB=(c)cos(A-B)

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  4. In DeltaABC, prove that: asinA-bsinB=csin(A-B

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  5. In DeltaABC, C=90^(@), A=30^(@), b=6, find the remaining elements of t...

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  6. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  7. In DeltaABC, if a = 2, b = 3, c = 4, prove that cosA=7/8.

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  8. If in DeltaABC, a=4,b=6,c=8 then 2cosA+4cosB+cosC=

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  9. In DeltaABC, if a=6, b=8, c=10, evaluate cos2A.

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  10. In DeltaABC, if b=7, c=24, a=25, find angleA.

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  11. In DeltaABC, a:b:c=15:7:13, find cosA.

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

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

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

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

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

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

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

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

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

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