What is the value of sin(135)-cos(30) ?

The value of sin(135)-cos(30) is (sqrt(2)-sqrt(3))/2

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sin(135)-cos(30)

sin (13 5^{\circ}) - cos (3 0^{\circ})

\frac{2 - 3}{2}

Solution steps

sin (13 5^{\circ}) - cos (3 0^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

= \frac{2}{2} - \frac{3}{2}

Simplify

\frac{2}{2} - \frac{3}{2} : \frac{2 - 3}{2}

= \frac{2 - 3}{2}

arctan (\frac{0}{1})

cot (42 0^{\circ})

tan (arcsin (\frac{4}{5}))

- 4 cos (0)

sin (7 7^{\circ})

What is the value of sin(135)-cos(30) ?
The value of sin(135)-cos(30) is (sqrt(2)-sqrt(3))/2