Trigonometric proof

Show that

where N is an integer to be found.

State the two values of x between 0° and 360° for which the value of N in part (b) is not valid.

Show that the expression

sin 2 θ cosec θ + cos 2 θ sec θ

can be written as

4 cos θ – sec θ

where sinθ ≠ 0 and cosθ ≠ 0

Explain why the student should reject one of their values for cosθ in Step 4.

State the correct solutions to the equation

Given that cos 1, prove the identity

Hence, find the set of values of A for which the equation

has real solutions.

Fully justify your answer.

Given that is obtuse and

find the exact value of cot

Given that

Express y in terms of sin .

Hence, prove that

Show that

Use the substitution

to show that

can be written as

where k is a constant to be found.

Hence, show

where c is a constant.

For cos 0, prove that