What is the value of sin(45)+cos(45) ?

The value of sin(45)+cos(45) is square root of 2

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sin(45)+cos(45)

sin (4 5^{\circ}) + cos (4 5^{\circ})

2

Solution steps

sin (4 5^{\circ}) + cos (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{2}{2} + \frac{2}{2}

Simplify

\frac{2}{2} + \frac{2}{2} : 2

= 2

arccos (0.2)

arctan (\frac{3}{3})

cos (12 0^{\circ}) + cos (4 5^{\circ})

cos (11 5^{\circ})

2 sin (2 π)

What is the value of sin(45)+cos(45) ?
The value of sin(45)+cos(45) is square root of 2