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

sin theta + sin (120^(@) + theta ) + sin ( theta - 120^(@)) =

Knowledge Check

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

    A
    A is true , R is true and R is correct explanation of A
    B
    A is true , R is true and R is not correct explanation of A
    C
    A is true , R is false
    D
    A is false , R is true

  • 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

    A
    only I is true
    B
    only II is true
    C
    both I & II are true
    D
    neither I nor II are true

  • 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

    A
    only I is true
    B
    only II is true
    C
    both I & II are true
    D
    neither I nor II are true

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