1

Problem

Find the value of (sin 45° + cos 45°) – (sin 30° + cos 60°).

2

Step

The given values are

(sin 45° + cos 45°) – (sin 30° + cos 60°)

3

Step

Simplify the equation:

\$1/\sqrt(2) + 1/\sqrt(2) - ( 1/2 + 1/2)\$

\$1/\sqrt(2) + 1/\sqrt(2) - 1\$

\$2 / \sqrt(2) -1 \$

4

Step

Make it simpler:

\$1/\sqrt(2) + 1/\sqrt(2) - 1\$

\$2 / \sqrt(2) -1 \$

5

Step

Do rationalisation and after simplification:

\$(2 / \sqrt(2)) \times (\sqrt (2)/ \sqrt(2)) - ((1 \times \sqrt(2))/ (\sqrt(2)))\$

\$(2 \sqrt(2)) /2 - 1 \$

\$(2\sqrt(2) - 2) / (2)\$

6

Step

Take common 2 and make it simplify:

\$2 ( (sqrt(2) -1 )/ (2))\$

\$sqrt(2) -1\$

7

Solution

Therefore, the value of (sin⁡45°+cos⁡45°) - (sin⁡30°+cos⁡60°)is \$\sqrt(2) -1\$.

8

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

9

Choice-A

Option A is not correct because it represents \$\sqrt(2) - 1\$, which does not match the computed value

Wrong 2

10

Choice-B

This is the incorrect expression and does not simplify to \$sqrt(2)+1\$

Wrong \$sqrt(2) +1\$

11

Choice-C

The expression is incorrect; it does not simplify to - 2

Wrong -2

12

Choice-D

Simplify this expression correctly to its simplest form: \$\sqrt(2) - 1\$

Correct \$sqrt(2) -1\$

13

Answer

Option

D

14

Sumup

Please summarize choices