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Prove that: i) sin(A+B)cos(A-B)-cos(A+...

Prove that:
i) `sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B`
ii) `cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)`

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Evaluate: i) sin48^(@)cos42^(@)+cos48^(@)sin42^(@) ii) cos72^(@)co...

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  2. Evaluate: i) cos75^(@) , ii) cos15^(@), iii) tan75^(@), iv) tan105^(@...

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  3. Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^...

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  4. If cosA=4/3 and cosB=12/13, then find the values of cos(A+B) and sin(A...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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