Trigonometric Functions of Multiple Angles

Prove the following:

`cos (pi/2 - x) cos(pi/2 - y) - sin(pi/2 - x) sin(pi/2 - y)` = – cos (x + y)

Prove the following:

tan8θ − tan5θ − tan3θ = tan8θ tan5θ tan3θ

Prove the following:

tan50° = tan40° + 2 tan10°

Prove the following:

cos(x + y).cos(x − y) = cos²y − sin²x

Find sin 2x, cos 2x, tan 2x if secx = `(-13)/5, pi/2 < x < pi`