What is the value of cos(45)(sin(30)+tan(60)) ?

The value of cos(45)(sin(30)+tan(60)) is (sqrt(2)(1+2sqrt(3)))/4

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cos(45)(sin(30)+tan(60))

cos (4 5^{\circ}) (sin (3 0^{\circ}) + tan (6 0^{\circ}))

\frac{2 ( 1 + 2 3 )}{4}

Solution steps

cos (4 5^{\circ}) (sin (3 0^{\circ}) + tan (6 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}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

= \frac{2}{2} (\frac{1}{2} + 3)

Simplify

\frac{2}{2} (\frac{1}{2} + 3) : \frac{2 ( 1 + 2 3 )}{4}

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

cos (16 5^{\circ}) - cos (1 5^{\circ})

2 sin (3 0^{\circ}) + 3 cos (6 0^{\circ}) - 3 tan (4 5^{\circ})

cos (arcsin (\frac{4}{5}) + arccos (\frac{3}{5}))

90 sin (6 0^{\circ})

cos (2) (90)

What is the value of cos(45)(sin(30)+tan(60)) ?
The value of cos(45)(sin(30)+tan(60)) is (sqrt(2)(1+2sqrt(3)))/4