Lesson Plan

• Describe the three fundamental trigonometric identities and how they are derived.
• Apply the identities to simplify algebraic trigonometric expressions.
• Solve trigonometric equations by substituting the appropriate identity.
• Prove derived identities and justify each transformation.

• Projector and screen
• Whiteboard and markers
• Worksheet with practice questions
• Scientific calculators
• Printed handout of the three identities
• Right‑angled triangle diagram

Begin with a quick visual of a right‑angled triangle to remind students how sine, cosine and tangent relate to side lengths. Ask them to recall the Pythagorean identity and predict how it might connect to secant, cosecant and cotangent. Explain that today they will master three key identities and use them to simplify, solve and prove further statements. Success will be measured by accurate simplifications and correct solutions to the practice problems.

1. Do‑now (5'): Simplify \(\frac{1}{\sec^{2}\theta}+\tan^{2}\theta\) using the given identities.
2. Mini‑lecture (10'): Derive the sec‑tan and csc‑cot forms by dividing the Pythagorean identity; emphasise each algebraic step.
3. Guided practice (15'): Work through Example 1 (simplification) and Example 2 (solving) together, checking for misconceptions.
4. Independent practice (15'): Students attempt practice questions 1‑4 on their worksheets while the teacher circulates.
5. Exit ticket (5'): Write one of the three identities from memory and give a brief example of its use.

Recap the three identities and highlight how they streamlined the examples and practice problems. Collect the exit tickets to gauge immediate understanding, and assign the remaining practice questions as homework, encouraging students to show each step clearly.