What is expand cos(105) ?

The solution to expand cos(105) is 1/(2sqrt(2))-(sqrt(3))/(2sqrt(2))

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expand cos(105)

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cos (10 5^{\circ})

\frac{1}{2 2} - \frac{3}{2 2}

Decimal Notation

- 0.25881 \dots

Solution steps

cos (10 5^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

= cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

= \frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

Simplify

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( 1 - 3 )}{4}

= \frac{2 ( 1 - 3 )}{4}

Simplify

= \frac{1}{2 2} - \frac{3}{2 2}

\frac{n}{( nb - 1 - ib ) i}

ln (\frac{6 x}{x - 6})

(\frac{( 1 + 5 )}{2})^{2}

\frac{3 x ^{3} - 4 x + 5}{( x - 1 ) ( x ^{2} + 2 x + 1 )}

\frac{2 x ^{2} + x + 8}{( x ^{2} + 4 ) ^{2}}

What is expand cos(105) ?
The solution to expand cos(105) is 1/(2sqrt(2))-(sqrt(3))/(2sqrt(2))