Trigonometric Identities Practice 3: Mixed Simplification

Practise focused skills from Trigonometric Identities

MathematicsGrade 10Mixed10 questions20 min

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Section A: Mixed Identity Use · 5 questionsSection B: Restrictions and Errors · 5 questions

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Section A: Mixed Identity Use

Simplify and prove with several identities.

Choose the best answer for each question.

Question 1

MediumQuestion

If $\sin A=\frac{8}{17}$ for acute $A$ , find $\cot A$ .

Topic: Expression Evaluation · Skill: Evaluate identities for given ratio values

Question 2

MediumQuestion

Simplify $\tan^2A+1-\sec^2A$ .

Topic: Identity Simplification · Skill: Simplify expressions using identities

Question 3

AdvancedQuestion

Which transformation proves $\frac{\cos A}{1-\sin A}=\frac{1+\sin A}{\cos A}$ ?

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

Question 4

MediumQuestion

Simplify $\frac{\sec A}{\tan A}$ .

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

Question 5

AdvancedQuestion

Simplify $\frac{1-\cos^2A}{1+\cos A}$ .

Topic: Identity Proofs · Skill: Prove identities using factorisation

What this assignment covers

Combine identities, factorisation and domain reasoning in mixed problems.

Skills and sections

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

Section A: Mixed Identity Use: 5 questions
Section B: Restrictions and Errors: 5 questions