Mathematics (AS)·Trigonometry · NSSCAS 1.6.3
Trigonometric identities & proof
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Where do the famous identities tan θ ≡ sin θ/cos θ and sin²θ + cos²θ ≡ 1 actually come from? In this lesson Miss Eve builds both of them from a simple right-angled triangle, then shows you her golden rules for proving identities line by line. You will prove three real exam-style identities, including a Stretch-level one with fractions. Then you will use the same two tools to solve trig equations for every angle in the range — without falling into the famous divide-by-sine trap.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.6.3):
- Use the identities tan θ ≡ sin θ / cos θ and sin²θ + cos²θ ≡ 1 to prove trigonometric identities, working on one side only
- Use the same identities to solve trigonometric equations by reducing the equation to a single ratio, factorising, and finding all solutions in the given range
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