Question

Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.

Answer 1

sec30° cosec60° + cos60° sin30°.

cos30° = `sqrt(3)/(2)`

⇒ sec30° = `(2)/sqrt(3)`

sin60° = `sqrt(3)/(2)`

⇒ cosec60° = `(2)/sqrt(3)`

cos60° = `(1)/(2) , sin30° = (1)/(2)`

sec30° cosec60° + cos60° sin30°

= `(2)/sqrt(3) xx (2)/sqrt(3) + (1)/(2) xx (1)/(2)`

= `(4)/(3) + (1)/(4)`

= `(16 + 3)/(12)`

= `(19)/(12)`.