Question

Evaluate each of the following:
cosec330°cos60°tan345°sin²90°sec²45°cot30°

Answer 1

cosec330°cos60°tan345°sin²90°sec²45°cot30° = 4√3 - 6

Given,

cosec 330° cos 60° tan 345° sin² 90° sec² 45° cot 30°

= cosec (360° - 30°) cos 60° tan (360° - 15°) sin² 90° sec² 45° cot 30°  

= - cosec 30° cos 60° (-tan 15°) sin² 90° sec² 45° cot 30°  

= -(2 ) (1/2 ) [-(2-√3) ] (1)^2 (√2)^2 ( √3)

= (-1) (-2+√3 ) (2) (√3)

= (-2√3) (-2+√3 )

= 4√3 - 2√3 (√3)

= 4√3 - 6