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If "cosec"A + secA="cosec"A+secB, prove ...

If `"cosec"A + secA="cosec"A+secB`, prove that:
`tanA.tanB=cot(A+B)/(2)`

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: (cos(60^(@)-A)+sin(30^(@)-A))/(cos(30^(@)-A)-sin(60^(@)-A)...

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

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

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

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

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

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

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

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  9. If tanB=(nsinAcosA)/(1-nsin^(2)A), prove that: tan(A-B)=(1-n)tanA

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  10. If 2tanB +cotB=tanA, prove that: 2tan(A-B)=cotB

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  11. i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin...

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  12. If A+B=225^(@), prove that: (cotA)/(1+cotA) xx (cotB)/(1+cotB) = 1/2

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  13. Prove that the value of 5 costheta+3 cos(theta+pi/3) lies between -7 a...

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  14. Prove that: sin2A+2sin4A+sin6A=4cos^(2)A.sin4A

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  15. Prove that: (sin7A+sin5A+sin9A+sin3A)/(cos3A+cos5A+cos7A+cos9A)= tan...

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  16. Prove that: sinA+sin2A+sin4A+sin5A= 4sin3A. cosA/2.cos(3A)/(2)

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  17. Prove that: (cos5A.cos8A-cos12A.cos9A)/(sin8A.cos5A+cos12A. sin9A)=t...

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  18. If cosA=kcos(A-2B), prove that: tan(A-B)tanB= (1-k)/(1+k)

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  19. If "cosec"A + secA="cosec"A+secB, prove that: tanA.tanB=cot(A+B)/(2)

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  20. If (sin(A+B))/(cos(A-B))=(1-m)/(1+m),then tan(pi/4-A)tan(pi/4-B)=?

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