1.

Sin(-11pi/3)tan(35pi/6)sec(-7pi/3)/cot (3pi/4)cosec(7pi/4)cos(11π/6)​

Answer»

To Find : Value of

SIN(-11π/3) . tan( 35π/6 ) . sec( -7π/3 ) . cot( 3π/4 ) . cosec( 7π/4 ) . COS( 11π/6 )

Solution :

GIVEN terms is sin(-11π/3) . tan( 35π/6 ) . sec( -7π/3 ) . cot( 3π/4 ) . cosec( 7π/4 ) . cos( 11π/6 )

Now ,

•sin( -11π/3 ) = -sin( 11π/3 )

= -sin( 4π - π/3 ) = sin(π/3) = √3/2

•tan( 35π/6 ) = tan( 6π-π/6)

= -tan(π/6) = -(1/√3) = -1/√3

• sec ( -7π/3 ) = sec( 7π/3 )

= sec( 2π + π/3 ) = sec ( π/3 ) = 2

• cot ( 3π/4 ) = cot ( π-π/4 )

= -cot(π/4) = -1

• cosec ( 7π/4 ) = cosec ( 2π - π/4 )

= - cosec ( π/4 ) = -√2

• cos ( 11π/6 ) = cos ( 2π - π/6 )

= cos ( π/6 ) = √3/2

•Now ,

sin(-11π/3) . tan( 35π/6 ) . sec( -7π/3 ) .cot( 3π/4 ) . cosec( 7π/4 ) . cos( 11π/6 ) = (√3/2)×(-1/√3)×(2)×(-1)×

(-√2)×(√3/2) = -√3/√2

•Hence , value of TERM is -√3/√2


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