Question

Sin(-11π/3)×tan(35π/6)×sec(-7π/3)÷cos(5π\4×cosec(7π\4)×cos(17π\6)

Answer 1

Given : Sin(-11π/3)×tan(35π/6)×sec(-7π/3)÷cos(5π\4×cosec(7π\4)×cos(17π\6)

To Find : Value / Simplify

Solution:

Sin(-11π/3)×tan(35π/6)×sec(-7π/3)÷cos(5π\4×cosec(7π\4)×cos(17π\6)

Sin(-11π/3)×tan(35π/6)×sec(-7π/3)

Sin(-11π/3)  = Sin(-11π/3 + 4π)   = Sin(π/3)  

tan(35π/6)  = tan(35π/6 -6π)  = tan(-π/6) = - tan(π/6) =  - cot(π/3)

sec(-7π/3) =sec(-7π/3  + 2π)  = sec(-π/3) = sec(π/3)  = 1/Cos(π/3)

Sin(π/3) ( - cot(π/3)) 1/Cos(π/3) = - 1

cos(5π\4)×cosec(7π\4)×cot(17π\6)

cos(5π\4) = cos(  π +π\4)  = - Cosπ\4

cosec(7π\4) = Cosec( -π\4) = - 1/Sin(π\4)

cos(17π\6)  = cos(5π\6) = cos(π- π\6)  = - cosπ\6

cos(5π\4)×cosec(7π\4)×cot(17π\6) =   cos( π\6)   as

Sin(-11π/3)×tan(35π/6)×sec(-7π/3)÷cos(5π\4×cosec(7π\4)×cos(17π\6)

= - 1/  -cos( π\6)

= -1 /(-√3/2)

=   2/√3

Sin(-11π/3)×tan(35π/6)×sec(-7π/3)÷cos(5π\4×cosec(7π\4)×cos(17π\6)=   2/√3

Learn More

tan 11 pi/3 - 2 sin 4 pi/6 - 3/4 cosec × cosec pi/4 + 4 cos × cos 17pi/6 ...

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