Trigonometric Proof (Edexcel A Level Maths: Pure): Exam Questions

Prove that

where .

Prove that

Prove that

where .

Show that

Show that

Prove that

where .

Prove that

Given that

• is small and in radians

• terms involving (or higher powers of ) can be ignored

show that

where and are constants to be found.

Show that the result in part (a) gives a percentage error of 0.583%, to 3 significant figures, when used to approximate

(i) Prove the identity

(ii) Use a counter example to disprove the statement

Prove that

Prove that

where .

Prove that

Use the identity

to show that

Show that

Use the identity

to show that

where and are constants to be found.

Given that is small, and that terms involving or higher powers of  can be ignored, show that

Find the percentage error when the result in part (a) is used to approximate

giving your answer correct to 3 significant figures.

Show that

Show that

where

Prove that

(i) Show that

where , and are integers to be found.

(ii) Use a counter example to disprove the statement

where , and are their values from part (i).

Show that

Prove that

Show that

where .

Show that

Show that

Consider the three triangles, all of height 1, as shown below.

By applying the area formula  to each one, prove the identity

Suggest one limitation of this proof.

Show that

Hence, or otherwise, show that

where

Prove that