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sin theta sin (60^(@) - theta) sin (60^(...

`sin theta sin (60^(@) - theta) sin (60^(@)+ theta) in [-k,k] rArr k=`

A

`1/2`

B

`1/3`

C

`1/4`

D

`3/4`

Text Solution

Verified by Experts

The correct Answer is:
C
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I : If ( 1+ tan A) (1+ tan B)=2 " then " A+B=45^(@) or 225^(@) II : sin^(2) theta + sin^(2) (60^(@) + theta ) + sin^(2) (60^(@) - theta ) = 3//2

I : cos^2 theta + cos^(2) (60^@ + theta ) + cos^(2) (60^@ - theta ) = 3//2 II : sin^(2) theta + sin^(2)(60^(@) + theta ) + sin^(2)(60^(@) - theta ) =3//2

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Prove that sinthetasin(60^(@)+theta)sin(60^(@)-theta)=1/4sin3theta Hence deduce that sin20^(@)sin40^(@)sin60^(@)sin80^(@)=3//16 (OCT-97,INST.93)

AAKASH SERIES-PERIODICITY AND EXTEME VALUES-PRACTICE SHEET (EXERCISE) LEVEL-I(MAIN) Extreme values ( Single answer type questions )
  1. sin theta sin (60^(@) - theta) sin (60^(@)+ theta) in [-k,k] rArr k=

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  2. The minimum and maximum values of sin^(4) x + cos^(4) x are

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  3. The range of sin^(6) x + cos^(6) x

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  4. 16 sin x cosx cos 2x cos 4x cos 8x in

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  5. The minimum and maximum values of sin^(2) (60^(@)-x) + sin^(2) ( 60^(@...

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  6. sin^(2) ( 60^(@) + x) sin^(2) ( 60^(@) - x) in [ - (k)/(2) , (k)/(2) ]...

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  7. The extreme values of 4cos(x^(2)).cos((pi)/(3)+x^(2)).cos((pi)/(3)-x^...

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  8. For all values of theta, the values of 3-cos theta+cos (theta+(pi)/(3)...

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  9. 5 cos theta + 3 cos ( theta - (pi)/(3) )+8 in

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  10. A+B = 90^(@) rArr cos A cos B in

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  11. A+B = 90^(@) rArr sin A + sin Bin

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  12. The minimum and maximum values of 8 cos 3x - 15 sin3x are

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  13. The maximum value of (3 ) /( 5 sin x-12 cos x+19) is

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  14. cos5x=16 cos^(5) x -20 cos^(3) x +5 cos x in

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

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  16. Minimum value of 9 sec^(2) theta + 4 cosec^(2) theta + 7 is

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  17. If a le 3 cos x + 5 sin ( x - pi//6) le b for all x , then ( a, b) is

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  18. cos^(2) (60^(@) - x) + cos^(2) (60^(@) +x) in

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  19. sin^(2) x + 4 sin x+5 in [k, 5k ] rArr k =

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  20. The least value of cos^(2) theta - 6 sin theta.cos theta+ 3 sin^(2) th...

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