Answer:
square root of 192
Step-by-step explanation:
12 cos 30 degrees + 2 tan 60 degrees
= 12* (root 3 /2) + 2* root 3 [as cos 30= root 3/2 and tan 60 = root 3]
=6 root 3 + 2 root 3
= 8 root 3
= square root of 64*3
=square root of 192
= square root of k [ where k = 192 = integer]
Trigonometry ratios are used to represent sine, cosine and tangent functions
The value of [tex]\mathbf{12cos(30) + 2tan(60)}[/tex] is [tex]\mathbf{\sqrt {192}}[/tex]
The trigonometry equation is given as:
[tex]\mathbf{12cos(30) + 2tan(60)}[/tex]
In trigonometry,
[tex]\mathbf{cos(30^o) = \frac{\sqrt 3}{2}}[/tex]
[tex]\mathbf{tan(60^o) = \sqrt 3}[/tex]
So, we have:
[tex]\mathbf{12cos(30) + 2tan(60) = 12 \times \frac{\sqrt 3}{2} + 2 \times \sqrt 3}[/tex]
Evaluate all products
[tex]\mathbf{12cos(30) + 2tan(60) = 6\sqrt 3 + 2 \sqrt 3}[/tex]
Add roots
[tex]\mathbf{12cos(30) + 2tan(60) = 8 \sqrt 3}[/tex]
Express 8 as square root of 64
[tex]\mathbf{12cos(30) + 2tan(60) = \sqrt {64} \times \sqrt 3}[/tex]
So, we have:
[tex]\mathbf{12cos(30) + 2tan(60) = \sqrt {64 \times 3}}[/tex]
Evaluate product
[tex]\mathbf{12cos(30) + 2tan(60) = \sqrt {192}}[/tex]
The form is given as:
[tex]\mathbf{\sqrt {k}}[/tex]
By comparison, we have:
[tex]\mathbf{k = 192}[/tex]
Hence, the value of [tex]\mathbf{12cos(30) + 2tan(60)}[/tex] is [tex]\mathbf{\sqrt {192}}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
