What is the value of sec((11pi)/6)sin(pi/6)+cos((7pi)/6) ?

The value of sec((11pi)/6)sin(pi/6)+cos((7pi)/6) is -(sqrt(3))/6

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sec((11pi)/6)sin(pi/6)+cos((7pi)/6)

sec (\frac{11 π}{6}) sin (\frac{π}{6}) + cos (\frac{7 π}{6})

- \frac{3}{6}

Solution steps

sec (\frac{11 π}{6}) sin (\frac{π}{6}) + cos (\frac{7 π}{6})

Rewrite using trig identities:

sec (\frac{11 π}{6}) = \frac{2 3}{3}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Rewrite using trig identities:

cos (\frac{7 π}{6}) = - \frac{3}{2}

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

Simplify

\frac{2 3}{3} \cdot \frac{1}{2} - \frac{3}{2} : - \frac{3}{6}

= - \frac{3}{6}

arccot (cot (- \frac{π}{4}))

arctan (1.49)

arctan (1.66)

sin (1) - \frac{1}{2}

arcsin (0.185)

What is the value of sec((11pi)/6)sin(pi/6)+cos((7pi)/6) ?
The value of sec((11pi)/6)sin(pi/6)+cos((7pi)/6) is -(sqrt(3))/6