How do you prove a trigonometric identity?

Start on one side and work step by step until you reach the other. Every step must itself be an identity, so that the chain holds for every value of the angle.

True or False? A trigonometric proof must start from the left-hand side.

False. Either end is a legitimate starting point, and the right-hand side is sometimes the easier one. What matters is starting from the more complicated side, since that is the one with something to simplify.

What makes trigonometric proofs involving fractions harder?

They often produce fractions within fractions, which have to be handled confidently. Multiplying numerator and denominator by the same expression usually clears them in a single step.

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Trigonometric Proof (Edexcel A Level Maths: Pure): Flashcards

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How do you prove a trigonometric identity?

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Cards in this collection (6)

How do you prove a trigonometric identity?
Start on one side and work step by step until you reach the other.
Every step must itself be an identity, so that the chain holds for every value of the angle.
True or False?
A trigonometric proof must start from the left-hand side.
False.
Either end is a legitimate starting point, and the right-hand side is sometimes the easier one.
What matters is starting from the more complicated side, since that is the one with something to simplify.
How does the target expression help you choose your next step in a proof?
It tells you which functions you have to end up with, so any identity moving you towards them is worth trying.
If the target is in $\tan$ alone, for instance, every $\sin$ and $\cos$ has to go.
How can a compound angle formula help prove an identity that contains no sum of angles?
By substituting cleverly: $x$ can be written as $(x + y) - y$ , or $2 x$ as $x + x$ .
That creates a compound angle where none was visible, which makes the formula available.
What makes trigonometric proofs involving fractions harder?
They often produce fractions within fractions, which have to be handled confidently.
Multiplying numerator and denominator by the same expression usually clears them in a single step.
You cannot see how to start a trigonometric proof. What is usually worth trying?
Write everything in terms of $\sin$ and $\cos$ .
That clears $\tan$ , $\sec$ , $cosec$ and $\cot$ in one move, and usually makes the structure obvious.

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