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If tanA=m/(m-1) and tanB=1/(2m-1), find ...

If `tanA=m/(m-1)` and `tanB=1/(2m-1)`, find the value of `tan(A-B)`.

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To find the value of \( \tan(A - B) \) given \( \tan A = \frac{m}{m - 1} \) and \( \tan B = \frac{1}{2m - 1} \), we can use the identity for the tangent of the difference of two angles: \[ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \] ### Step 1: Substitute the values of \( \tan A \) and \( \tan B \) ...
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. If tanA=2, secB=-5/3, where pi lt A lt (3pi)/(2), pi/2 lt B lt pi, the...

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  2. If cosA=-sqrt(3)/2, sinB=-5/13, where pi/2 lt A lt pi, (3pi)/(2) lt B ...

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  3. If tanA=m/(m-1) and tanB=1/(2m-1), find the value of tan(A-B).

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

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

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

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

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

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

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

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

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

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

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  14. If A-B=pi/4, then prove that: (1+tanA)(1-tanB)=2

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

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

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

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

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

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

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