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If sec alpha = (13)/(5) " where " alpha...

If ` sec alpha = (13)/(5) " where " alpha lt 90^(@) , ` then the value of `(2-3 cot alpha )/(4-9 tan alpha ) = `

A

`-15//352`

B

`15//352`

C

`13//352`

D

none

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)
  1. If theta lies in the first quadrant and 5 tan theta = 4 , " then "...

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  2. If cot theta = (b)/a " then " ( a sin theta - b cos theta )/( a sin t...

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  3. If sec alpha = (13)/(5) " where " alpha lt 90^(@) , then the value ...

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  4. If cot theta = sqrt(7) and theta does not lie the first quadrant , t...

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  5. If cos theta =(3)/5 and theta is not in the first quadrant , then (...

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  6. If tan theta = -(5)/(12) and theta is not in the fourth quadrant th...

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  7. If 90^(@) lt A lt 180^(@) , 180^(@) lt B lt 270^(@) and cos A=-(sqrt(3...

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  8. If 180^(@) lt A lt 270^(@) , 270^@ lt B lt 360^(@) and sin A = -5//13...

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  9. If 13 sin A = 12 , pi//2 lt A lt pi and 3 sec B=5 , 3pi/2 lt B lt 2p...

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  10. 3[sin^(4)(3pi//2-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)(pi//2+alpha)+sin...

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  11. If sin (alpha+beta ) =1 , sin (alpha-beta ) =1//2 " then " tan (alpha...

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  12. ( sin theta + " cosec " theta )^(2) + ( cos theta + sec theta )^(2)=

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  13. (cos theta + sin theta )^(2) + (cos theta - sin theta )^(2) =

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  14. ( tan alpha + " cosec " beta )^(2) - ( cot beta - sec alpha )^(2) =

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  15. (sec alpha * sec beta + tan alpha tan beta )^(2)-( sec alpha * tan be...

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  16. (sec A + tan A -1) (sec A - tan A+1)=

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  17. ("cosec " theta - sin theta ) ( sec theta - cos theta ) ( tan theta + ...

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  18. 2(sin^(6) x + cos^(6) x ) -3(sin^(4) x + cos^(4) x ) +1=

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  19. 3(sin x + cos x )^(4) + 6(sin x - cos x )^(2) + 4(sin^(6) x + cos^(6) ...

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  20. sin A ( cot A +3( 3 cot A + 1) -1 " cosec " A -10 cos A =

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