What is the value of cos(45)-sin(30) ?

The value of cos(45)-sin(30) is (sqrt(2)-1)/2

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cos(45)-sin(30)

cos (4 5^{\circ}) - sin (3 0^{\circ})

\frac{2 - 1}{2}

Solution steps

cos (4 5^{\circ}) - sin (3 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{2}{2} - \frac{1}{2}

Simplify

\frac{2}{2} - \frac{1}{2} : \frac{2 - 1}{2}

= \frac{2 - 1}{2}

sin (7 0^{\circ}) 20

sin (9 0^{\circ}) - sin (- 9 0^{\circ})

2 cot (4 5^{\circ})

\frac{tan ( \frac{0.75 π}{2} )}{tan ( \frac{0.5 π}{2} )}

arccsch (2)

What is the value of cos(45)-sin(30) ?
The value of cos(45)-sin(30) is (sqrt(2)-1)/2