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If tanA=m+1 and tanB=m-1, prove that tan...

If `tanA=m+1` and `tanB=m-1`, prove that `tan(A-B)=2/(m^(2))`.

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. If tanA=m/(m-1) and tanB=1/(2m-1), find the value of (tanA-B).

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  2. If tanA=m/(m-1) and tan(B)=n, find the values of tan 2A and tan 2B.

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  3. If tanA=m+1 and tanB=m-1, prove that tan(A-B)=2/(m^(2)).

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  4. Prove that: (tan(pi/4+A))/(tan(pi/4-A))=((1+tanA)/(1-tanA))^(2)

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  5. Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

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  6. Prove that: cos((3pi)/(4)+A)-cos((3pi)/(4)-A)=-sqrt(2)sinA

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  7. Prove that: sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2)=1/sqrt(2)sinA

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  8. Prove that: sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/8+sin^(2)(7pi)...

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  9. Prove that: cos^(2)pi/8 + cos^(2)(3pi)/(8) + cos^(2)(5pi)/(8)+ cos^(...

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  10. Prove that: i) tan36^(@)+tan9^(@)+tan36^(@)tan9^(@)=1

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  11. Prove that: (cos8^(@)-sin8^(@))/(cos8^(@)+sin8^(@))=cot53^(@)

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  12. If A-B=pi/4, then prove that: (1+tanA)

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  13. Prove that: (cos(60^(@)-A)+sin(30^(@)-A))/(cos(30^(@)-A)-sin(60^(@)-A)...

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  14. i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2

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  15. Prove that: (tan(pi/4+A)+tan(pi/4-A))/(tan(pi/4+A)-tan(pi/4-A))="cos...

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  16. Prove that: (sin(A-B))/(cosAcosB)+(sin(B-C))/(cosBcosc)+(sin(C-A))/(...

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  17. Prove that: sinAsin(B-C)+sinBsin(C-A)+sinCsin(A-B)=0

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  18. Prove that: cot2Acot3A-cot3Acot5A-cot5Acot2A=1

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  19. Prove that: cotA-cot2A="cosec"2A

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  20. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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