Question

Without using mathematical tables, evaluate, `2sqrt(2)  cos 45^circ  cos 60^circ +  2sqrt(3)  sin 30^circ  tan 60^circ -  cos 0^circ`.

Answer 1

Given: `2sqrt(2)  cos 45^circ  cos 60^circ +  2sqrt(3)  sin 30^circ  tan 60^circ -  cos 0^circ`

Step-wise calculation:

1. Substitute exact values:

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

`cos 60^circ = 1/2`

`sin 30^circ = 1/2`

`tan 60^circ = sqrt(3)`

cos 0° = 1

2. Evaluate term-by-term:

Term 1: `2sqrt(2) xx sqrt(2)/2 xx 1/2`

= `2sqrt(2) xx sqrt(2)/4` 

= `2 xx 2/4`

= 1

Term 2: `2sqrt(3) xx 1/2 xx sqrt(3)` 

= `2sqrt(3) xx sqrt(3)/2` 

= `2/2 xx 3`

= 3

Term 3: –cos 0° = –1.

3. Sum: 1 + 3 – 1 = 3.

The value of the expression is 3.