What is the value of tan(pi/6)+sin((5pi)/3)*cos(-(3pi)/4) ?

The value of tan(pi/6)+sin((5pi)/3)*cos(-(3pi)/4) is (sqrt(3))/3+(sqrt(6))/4

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tan(pi/6)+sin((5pi)/3)*cos(-(3pi)/4)

tan (\frac{π}{6}) + sin (\frac{5 π}{3}) \cdot cos (- \frac{3 π}{4})

\frac{3}{3} + \frac{6}{4}

Solution steps

tan (\frac{π}{6}) + sin (\frac{5 π}{3}) cos (- \frac{3 π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{3 π}{4}) = cos (\frac{3 π}{4})

= tan (\frac{π}{6}) + sin (\frac{5 π}{3}) cos (\frac{3 π}{4})

Rewrite using trig identities:

sin (\frac{5 π}{3}) = 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

= tan (\frac{π}{6}) + 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6}) cos (\frac{3 π}{4})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

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

Simplify

\frac{3}{3} + 2 \cdot \frac{1}{2} (- \frac{3}{2}) (- \frac{2}{2}) : \frac{3}{3} + \frac{6}{4}

= \frac{3}{3} + \frac{6}{4}

sec (53.1 3^{\circ})

arctan (\frac{7}{14})

\frac{8}{cos ( 6 5 ^{\circ} )}

sin (1 - \frac{π}{2})

arccos (\frac{16}{20})

What is the value of tan(pi/6)+sin((5pi)/3)*cos(-(3pi)/4) ?
The value of tan(pi/6)+sin((5pi)/3)*cos(-(3pi)/4) is (sqrt(3))/3+(sqrt(6))/4