Question

Sin(-660)×tan(1050)×sec(-420)/cos(225)× cosec(315)×cos(510)

Answer 1

Answer:

Find value of [sin(-660)tan(1050)sec(-420)] /  

[cos (225) cosec(315) cos (510)]

sin(-660°)    

= -Sin(660°)    sin (-θ)  = - sin θ

= -Sin(720° - 60°)  

= -Sin(2*360° - 60°)  

= -(-Sin60)       sin (n ∙ 360° - θ) = - sin θ

= Sin60°  = √3/2

tan(1050°) = tan(1080° - 30°)  

tan(3 * 360° - 30°) = -tan30°      (tan (n ∙ 360° - θ) = - tan θ)

= -1/√3

sec(-420°) = Sec420° = Sec(360° + 60°) = Sec60°  = 1/Cos60°  = 2

Numerator = (√3/2)(-1/√3)(2) = -1

Denominator

cos (225°) = Cos (180° + 45°) = Cos45°  = 1/√2

cosec(315) = Cosec(360° - 45°) = Cosec45° = 1/Sin45° = √2

Cos(510°) = Cos(360° + 150°) = Cos(150°) = Cos(180°-30°) = -Cos30° = -√3/2

Denominator = (1/√2)(√2)(-√3/2) = -√3/2

Numerator/Denominator =  (-1)/(-√3/2)  = 2/√3

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