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 -1/6

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

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

- \frac{1}{6}

Solution steps

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

Use the following trivial identity:

sin (π) = 0

= \frac{sec ( 11 π )}{6} \cdot \frac{0}{6} + \frac{cos ( 7 π )}{6}

Simplify

= \frac{cos ( 7 π )}{6}

Rewrite using trig identities:

cos (7 π) = - 1

= \frac{- 1}{6}

Simplify

= - \frac{1}{6}

sin (2 arctan (\frac{2}{3}))

- arctan (tan (\frac{2 π}{7}))

\frac{40}{cos ( 3 0 ^{\circ} )}

arctan (\frac{- 4}{5})

- sec (\frac{11 π}{6}) tan (\frac{11 π}{6})

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 -1/6