show that cos 300 degree cot 300 degree tan negative 420 degree by sin 135 degree sec 225 degree cosec 240 degree is equal to root 3 by 4
Answers
Given : cos 300° . Cot 300° . Tan (-420°) / Sin 135°. Sec 225° . cosec 240°
To Find : Show that value is √3/4
Solution:
cos 300° = Cos(-60°) = Cos 60° = 1/2
Cot 300° = Cot (-60°) = - cot60° = - 1/√3
Tan (-420°) = tan(-60°) = - tan60° = -√3
cos 300° . Cot 300° . Tan (-420°) = (1/2) (- 1/√3)(√3) = 1/2
Sin 135° = Sin 45° = 1/√2
Sec 225° = - sec 45° = -√2
cosec 240° = -cosec 60° - 2/√3
Sin 135°. Sec 225° . cosec 240° = (1/√2)( -√2)(- 2/√3) = 2/√3
cos 300° . Cot 300° . Tan (-420°) / Sin 135°. Sec 225° . cosec 240°
= (1/2) / (2/√3)
= √3/4
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