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Solution:
[tex]\[
\begin{aligned}
2 \tan 45^{\circ} + \cos 30^{\circ} - \sin 60^{\circ} \\
& = 2 \times 1 + \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} \\
& = 2 + 0 \\
& = 2
\end{aligned}
\][/tex]


Sagot :

Let's work through the solution step by step.

1. Calculate [tex]\(\tan 45^\circ\)[/tex]:

We know that [tex]\(\tan 45^\circ = 1\)[/tex].

2. Calculate [tex]\(\cos 30^\circ\)[/tex]:

The value of [tex]\(\cos 30^\circ\)[/tex] is given by the trigonometric table as [tex]\(\cos 30^\circ = \frac{\sqrt{3}}{2}\)[/tex].

3. Calculate [tex]\(\sin 60^\circ\)[/tex]:

Similarly, [tex]\(\sin 60^\circ\)[/tex] is given by [tex]\(\sin 60^\circ = \frac{\sqrt{3}}{2}\)[/tex].

4. Multiply [tex]\(2\)[/tex] by [tex]\(\tan 45^\circ\)[/tex]:

So, [tex]\(2 \times \tan 45^\circ = 2 \times 1 = 2\)[/tex].

5. Sum and subtract the trigonometric values:

Now let's put it all together:

[tex]\[ 2 \tan 45^\circ + \cos 30^\circ - \sin 60^\circ \][/tex]

Substituting the values we calculated:

[tex]\[ = 2 \times 1 + \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} \][/tex]

Simplify the expression inside the equation:

[tex]\[ = 2 + \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} \][/tex]

6. Final Simplification:

Since [tex]\(\frac{\sqrt{3}}{2}\)[/tex] and [tex]\(\frac{\sqrt{3}}{2}\)[/tex] cancel each other out:

[tex]\[ = 2 \][/tex]

So, the complete and final solution is:

[tex]\[ 2 \tan 45^\circ + \cos 30^\circ - \sin 60^\circ = 2 \][/tex]
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