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If tan A + tan B=p and cot A+ cot B=q th...

If `tan A + tan B=p and cot A+ cot B=q` then ` cot (A+B)=`

A

`(p-q)/(pq)`

B

`(q-p)/(pq)`

C

`(pq)/(p+q)`

D

`(pq)/(p-q)`

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 2 ( SPEICAL TYPE QUESTIONS ) SET -4
  1. If tan A + tan B=p and cot A+ cot B=q then cot (A+B)=

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  2. A : sin theta + sin (pi+ theta ) + sin ( 2pi + theta ) ......... + si...

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  3. A : sqrt(1-sin^(2)100^@) sec 100^(@) =-1 R : sqrt(x^(2))=-x " if "...

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  4. A : sin^(2) 5^(@) + sin^(2) 10^(@) + ..... + sin^(2) 85^(@) =17//2 ...

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  5. A : If sin x + " cosec "x=2 , " then " sin^(n)x+"cosec"^(n)x=2 R : ...

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  6. A : cos 20^(@) + cos 100^(@) + cos 140^(@) =0 . R : cos theta + co...

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  7. A : sin 40^@ - sin 80^(@) + sin 160^(@) = 0 R : sin theta + sin(60^...

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  8. A : tan ( alpha - beta ) + tan ( beta - alpha ) + tan ( gamma - alpha...

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  9. A : If cos (x-y) =3 cos ( x+y) " then " cot x - cot y=2 R : If (a)/...

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  10. A : If cot A + cot B + cos C = sqrt(3) " then " Delta ABC is an equi...

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  11. A : cos 40^(@) cos 80^(@) cos 160^(@) =-1//8 R : cos theta cos (120...

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  12. A : cos 24^(@) cos 48^(@) cos 96^@ cos 168^(@) = 1//16 R : cos x ...

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  13. A : tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 tan 8 theta - 16 co...

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  14. A : cos^(3) x + cos^(3)(120^@ + x) + cos^(3)(120^(@) - x)=(3)/(4) cos...

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  15. A : If x+y+z=xyz " then " sum(3x-x^(3))/(1-3x^(2))=Pi(3x-x^(3))/(1-3x^...

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  16. A : If x=sin(alpha - beta ) sin (gamma - delta), y=sin(beta - gamma ) ...

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  17. A : sum(r=1)^(n-1) cos^(2) (rpi)/(n)=(n)/(2)-1 R : cos alpha + cos...

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  18. Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to...

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  19. A : If A+B+C=180^(@) " then " cos^(2) A + cos^(2) B+ cos^2 C =1-2 cos ...

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  20. A : Period of sin8x+ cos 2x is pi R : Period of sin ax or cos ax "...

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  21. Assertion (A ) : The maximum value of 2 cos^(2) theta + sqrt(5) cos ...

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