Topic explanation

Standard explanation

Typical tasks: expand sin(A+B); tan(A+B); allied reduce; product-to-sum; sum-to-product; a numerical 1575 angle. Quote the exact identity the question needs. Check even/odd for negatives.

Key points

• compound: mixed products
• CAST for allied signs
• (sqrt(6)-sqrt(2))/4
• cos sum has a minus
• EXAM RESPONSE (FUNDAMENTALS OF TRIGONOMETRY): Typical tasks: expand sin(A+B); tan(A+B); allied reduce; product-to-sum; sum-to-product; a numerical
• 1. COMPOUND: Write the full four-term or tan fraction. 75=45+30, 15=45-30. Double if 2A appears.
• 2. ALLIED AND SUM/PRODUCT: Reduce to 30/45/60. Product 2 sin cos. Sum 2 sin(avg) cos(half). Cos-cos minus.
• WHAT — EXAM RESPONSE (FUNDAMENTALS OF TRIGONOMETRY): Typical tasks: expand sin(A+B); tan(A+B); allied reduce; product-to-sum; sum-to-product; a numerical

Labelled diagram