Determine the exact value of the expression using the half-angle formula.

tan (5π/6)

Write the given trigonometric function in terms of $\sec x$.

$\tan x$

Determine the exact value of the given trigonometric expression using the half-angle identity.

$\sin 67.5°$

Write the given trigonometric expression in terms of cosine.

cos 70° cos 10° + sin 70° sin 10°

Determine the exact value of the following trigonometric expression.

$\sin25\degree\cos65\degree+\cos25\degree\sin65\degree$

Find the exact value of $\cos\left(x-y\right)$ . Use a trigonometric identity.

$\cos x=\frac{5}{11}$, $\sin y=-\frac18$, $x$ in fourth quadrant, $y$ in third quadrant

Determine the exact value of the expression using the provided data. 

tan 2β where cosβ = 21/29, β lies in quadrant IV.

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

sin 2x = 2cos x