Sin(-11pi/3)tan(35pi/6)sec(-7pi/3)/cot (3pi/4)cosec(7pi/4)cos(11π/6)
Answers
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
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
Step-by-step explanation: