Question

Evaluate: sec 60° . cos² 30° + sin² 45°

Answer 1

`sec 60^circ = 1/(cos 60^circ)`

= `1/(1/2)`

= 2

`cos 30^circ = sqrt(3)/2`

`cos^2 30^circ = (sqrt(3)/2)^2`

= `3/4`

`sin 45^circ = sqrt(2)/2`

`sin^2 45^circ = (sqrt(2)/2)^2`

= `1/2`

Now, sec 60° . cos² 30° + sin² 45°

= `2 xx 3/4 xx 1/2`

= `6/4 + 1/2`

= `3/2 + 1/2`

= `4/2`

= 2