Question

Without using trigonometrical tables, evaluate:

`cosec^2 57^circ - tan^2 33^circ + cos 44^circ cosec 46^circ - sqrt(2) cos 45^circ - tan^2 60^circ`

Answer 1

`cosec^2 57^circ - tan^2 33^circ + cos 44^circ cosec 46^circ - sqrt(2) cos 45^circ - tan^2 60^circ`

= `cosec^2 (90^circ - 33^circ) - tan^2 33^circ + cos 44^circ cosec(90^circ - 44^circ) - sqrt(2) cos45^circ - tan^2 60^circ`

= `sec^2 33^circ - tan^2 33^circ + cos 44^circ sec 44^circ - sqrt(2) cos 45^circ - tan^2 60`

= `1 + 1 - sqrt(2) cos 45^circ -  tan^2 60`

= `1 + 1 - sqrt(2)(1/(sqrt2)) - (sqrt3)^2`

= 2 – 1 – 3

= – 2