Verified answer

Given :

[tex]sin \: 30° + sin \: 90° + cos \: 45°[/tex]

Values :

[tex]sin \: 30° = \frac{1}{2} \\ \\ sin \: 90° = 1 \\ \\ cos \: 45° = \frac{1}{ \sqrt{2} } [/tex]

Solution Explanation :

[tex]sin \: 30° + sin \: 90° + cos \: 45° \\ \\ = \frac{1}{2} + 1 + \frac{1}{ \sqrt{2} } \\ \\ = \frac{1}{2} + \frac{1}{1} + \frac{1}{ \sqrt{2} } \\ \\ = \frac{ \sqrt{2} + 2 \sqrt{2} + 2 }{2 \sqrt{2} } \\ \\ = \frac{4 \sqrt{4} }{2 \sqrt{2} } \\ \\ = 2 \sqrt{2} [/tex]

Answer:

The simplified expression is (3 + √2)/2.

Step-by-step explanation:

To calculate the values of sin(30°), sin(90°), and cos(45°), we can use the trigonometric identities:

sin(30°) = 1/2

sin(90°) = 1

cos(45°) = √2/2

Now, we can substitute these values into the expression:

sin(30°) + sin(90°) + cos(45°) = 1/2 + 1 + √2/2

To simplify the expression, we need to find a common denominator for the fractions:

= (1/2 + √2/2 + 2/2)

= (1/2 + √2/2 + 2)/2

Combining the numerators:

= (1 + √2 + 2)/2

= (3 + √2)/2

Thus, the simplified expression is (3 + √2)/2.

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