Trigonometric Identities Practice 2: Proof Techniques

Practise focused skills from Trigonometric Identities

MathematicsGrade 10Mixed10 questions20 min

Print / Save as PDF

Preview

Preview questions

Sample preview - start assignment to submit answers.

Focus question style

Section A: Proof Moves · 5 questionsSection B: Evaluation and Validity · 5 questions

Preview onlyStart free practice to answer.

Section A: Proof Moves

Choose useful transformations for identity proofs.

Choose the best answer for each question.

Question 1

MediumQuestion

Simplify $\cosec^2A-\cot^2A$ .

Topic: Identity Simplification · Skill: Simplify expressions using identities

Question 2

MediumQuestion

Which first step is useful to prove $\frac{1-\cos^2A}{\sin^2A}=1$ ?

Topic: Identity Proofs · Skill: Prove simple one-sided identities

Question 3

AdvancedQuestion

To prove $\frac{\sec^2A-1}{\sec^2A}=\sin^2A$ , which identity is most useful?

Topic: Identity Proofs · Skill: Prove simple one-sided identities

Question 4

MediumQuestion

Which replacement correctly uses reciprocal ratios?

Topic: Identity Proofs · Skill: Prove identities using reciprocal ratios

Question 5

AdvancedQuestion

Simplify $\sin A\cdot\cosec A$ where defined.

Topic: Identity Proofs · Skill: Prove identities using reciprocal ratios

What this assignment covers

Practise one-sided proofs, reciprocal substitutions and factorisation.

Skills and sections

Simplify expressions using identities, Prove simple one-sided identities, Prove identities using reciprocal ratios, Prove identities using factorisation, Evaluate identities for given ratio values

Section A: Proof Moves: 5 questions
Section B: Evaluation and Validity: 5 questions