Compound & double angle formulae

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

Show that

Hence solve, for 0 θ 180

giving your answers to one decimal place, where appropriate.

In this question you should show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Given that 1 + cos 2θ + sin 2θ ≠ 0 prove that

Hence solve, for 0 < x < 180°

giving your answers to one decimal place where appropriate.

Solve, for –180° θ 180°, the equation

giving your answers, where necessary, to one decimal place.

[ Solutions based entirely on graphical or numerical methods are not acceptable. ]

Deduce the smallest positive solution to the equation

Given that

show that

where A is a rational constant to be found.

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 < x < the equation

Give any non-exact answer to 3 decimal places where appropriate.

Given that

use standard trigonometric identities, to find in terms of p,

cot(– 45)°

Write each answer in its simplest form.

Prove that

Hence solve, for 0 ≤ θ < 2,

Give your answers to 3 decimal places.

Given that

Show, without using a calculator, that

Hence solve, for 0 < 360,

giving your answers to 1 decimal place.

Use an appropriate double angle formula to show that

and state the value of the constant /. (3)

You must show all your working. Give your answers in terms of z. (6)

Without using a calculator, find the exact value of

You must show each stage of your working.

Show that cos 2 + sin = 1 may be written in the form

Hence solve, for 0 < 360°, the equation

Express 4cosec² 2 − cosec² in terms of sin and cos .

Hence show that

Hence or otherwise solve, for 0 < <,

giving your answers in terms of .

f (x) = 7 cos 2x − 24sin 2x Given that f (x) = R cos(2x + α), where R 0 and 0 α 90,

find the value of R and the value of .

Hence solve the equation

for 0 ≤ x180, giving your answers to 1 decimal place.

Express 14cos² x 48sin x cos x in the form a cos 2x + bsin 2x + c, where a, b, and c are constants to be found.

Hence, using your answers to parts (a) and (c), deduce the maximum value of

Prove that

Hence, or otherwise,

show that tan 15° = 2 – ¥ 3,

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

Show that

Hence find, for –180° θ 180°, all the solutions of

Give your answers to 1 decimal place.

Use the identity cos(A + B) = cos Acos B sin Asin B, to show that

The curves C₁ and C₂ have equations

Show that the x-coordinates of the points where C₁ and C₂ intersect satisfy the equation

Express 4cos2x + 3sin 2x in the form R cos (2x – α), where R > 0 and 0 < α < 90°, giving the value of α to 2 decimal places.

Hence find, for 0 x 180°, all the solutions of

giving your answers to 1 decimal place.

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.

By writing 3 = (2 + ), show that

Hence, or otherwise, for 0 solve

Give your answers in terms of π.

Using sin( ) sin cos cos sin , or otherwise, show that