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( tan^(3) theta )/( 1+ tan^(2) theta )+ ...

`( tan^(3) theta )/( 1+ tan^(2) theta )+ ( cot^(3) theta )/( 1+ cot^(2) theta )= `

A

`sec theta * " cosec " theta -2 tan theta cot theta `

B

`sec theta * " cosec " theta - 2 sin theta cos theta `

C

sin theta * cos theta - 2 sec theta " cosec " theta `

D

`tan theta * cot theta -2 sec theta " cosec " theta `

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)
  1. (sin^(2) theta )/(1- cot theta )+(cos^(2) theta )/( 1- tan theta ) =

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  2. ( cos^(3 ) theta )/( 1 + sin theta ) + ( sin^(3) theta )/( 1- cos thet...

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  3. ( tan^(3) theta )/( 1+ tan^(2) theta )+ ( cot^(3) theta )/( 1+ cot^(2)...

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  4. ( cos^(3) A + sin^(3) A )/( cos A + sin A ) + (cos^(3) A - sin^(3)A)/(...

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  5. 1-(sin^(2)y)/(1+ cos y) + (1+ cosy)/( sin y) - (siny)/(1- cos y) =

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  6. ((sqrt(3) + 2 cosA)/( 1-2 sin A ))^(-3) + ((1+ 2 sin A )/( sqrt(3)-2 c...

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  7. sin^(4) theta + 2 sin^(2) theta (1-(1)/("cosec"^(2) theta ) )+ cos^(4)...

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  8. If "cosec" theta + cot theta = -3//2 , then " cosec " theta =

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  9. If " cosec " theta - cot theta =1//3 then theta lies in the quadran...

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  10. If sec theta - tan theta =4//3 , then sin theta =

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  11. If cos theta - sin theta = sqrt(2) sin theta " then " cos theta + si...

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  12. cos theta - 4 sin theta = 1 implies sin theta + 4 cos theta =

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  13. If tan theta + cot theta =2 , " then " sin theta =

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  14. If sec theta + tan theta = p(p ne 0) , then sin theta =

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  15. If a = sin theta + cos theta , b =sin^(3) theta + cos^(3) theta , th...

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  16. sin theta + cos theta = p , sin^(3) theta + cos^(3) theta = qimpliesp(...

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  17. If sin theta + cos theta = a " then " sin^(4) theta + cos^(4) theta =

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  18. If a cos theta + b sin theta = c " then " (a sin theta - b cos theta...

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  19. If x=a ( " cosec " alpha + cot alpha) and y=(b(1- cos alpha))/(sin al...

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  20. If sec theta + cos theta =1 , " then " sec^(3) theta + cos^(3) theta...

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