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If tanA=2, secB=-5/3, where pi lt A lt (...

If `tanA=2, secB=-5/3`, where `pi lt A lt (3pi)/(2)`, `pi/2 lt B lt pi`, then
i) Find the value of `tan(A+B)`,
ii) find the quadrant in which (A+B) terminates.

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AI Generated Solution

To solve the problem, we need to find the value of \( \tan(A + B) \) and determine the quadrant in which \( A + B \) terminates. ### Step 1: Find \( \tan A \) and \( \tan B \) We are given: - \( \tan A = 2 \) - \( \sec B = -\frac{5}{3} \) ...
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^...

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  2. If cosA=4/5 and cosB=12/13, then find the values of cos(A+B) and sin(A...

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  3. If tanA=2, secB=-5/3, where pi lt A lt (3pi)/(2), pi/2 lt B lt pi, the...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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