Secant, cosecant and cotangent

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

Show that cosecθ − sinθ ≡ cosθcotθ θ ≠ (180n)° n

Hence, or otherwise, solve for 0 < x < 180° cosec x − sin x = cos x cot (3 x − 50°)

Solve, for 0≤ θ <360°, the equation

giving your answers to one decimal place.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

Prove that

Hence solve, for 0 ≤ θ < 2,

Give your answers to 3 decimal places.

Given that

Hence show that

Find an expression for in terms of x. Give your answer in its simplest form.

Prove that

Hence, or otherwise,

show that tan 15° = 2 – ¥ 3,

solve, for 0 x 360°, cosec 4 x – cot 4 x = 1

By writing sec x as , show that sec x tan x.

Given that y = e^2x sec 3x,

The curve with equation y = e^2x sec 3x, − x , has a minimum turning point at (a, b).

Find the values of the constants a and b, giving your answers to 3 significant figures.

Write down sin 2 x in terms of sin x and cos x.

Find, for 0 < x < π, all the solutions of the equation

giving your answers to 2 decimal places.