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If 90^(@) lt A lt 180^(@) , 180^(@) lt B...

If `90^(@) lt A lt 180^(@) , 180^(@) lt B lt 270^(@) and cos A=-(sqrt(3))/(2) , sin B=-(3)/(5) "then" ( 2 tan B + sqrt(3) tan A)/( cot^(2) A + cos B) =`

A

`5//22`

B

`-5//22`

C

`22//5`

D

`-22//5`

Text Solution

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

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

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

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

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  5. 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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  6. 3[sin^(4)(3pi//2-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)(pi//2+alpha)+sin...

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

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

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

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

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

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

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

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  14. 2(sin^(6) x + cos^(6) x ) -3(sin^(4) x + cos^(4) x ) +1=

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  15. 3(sin x + cos x )^(4) + 6(sin x - cos x )^(2) + 4(sin^(6) x + cos^(6) ...

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

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  17. a sin^(2) theta + b cos^(2) theta =c implies tan^(2) theta =

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  18. sec^(4) theta (1-sin^4 theta ) - tan^(2) theta =

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  19. "cosec"^(2) theta * cot^(2) theta -sec^(2) theta * tan^(2) theta - (co...

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  20. sec^(2)A tan^(2) B-tan^(2)A sec^(2) B=

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