Question

Without using tables, evaluate the following: cosec³30° cos60° tan³45° sin²90° sec²45° cot30°.

Answer 1

cosec³30° cos60° tan³45° sin²90° sec²45° cot30°.

sin30° = `(1)/(2)`
cosec30° = 2

cos60° = `(1)/(2)`
sec60° = 2

cos45° = `(1)/sqrt(2)`
sec45° = `sqrt(2)`
tan45° = 1
sin90° = 1

tan30° = `(1)/sqrt(3)`
⇒ cot30° = `sqrt(3)`
cosec³30° cos60° tan³45° sin²90° sec²45° cot30°

= `(2)^3(1/2)(1)^3(1)^2(sqrt(2))^2(sqrt(3))`

= `8 xx (1)/(2) xx 2 xx sqrt(3)`
= `8sqrt(3)`.