alleryStart learning →If factoring and substitution both fail while verifying an identity, what is the recommended fallback?
AConvert every term to sines and cosines
BConvert every term to secants and cosecants
CDifferentiate both sides and compare them
DReplace the variable with a special angle
Answer & Solution
Correct answer: A. Convert every term to sines and cosines
1. The verification routine is to work one side, look for factoring or a squared binomial, then match functions to known identities.
2. When none of that lands, rewrite every term using only sine and cosine.
3. Sine and cosine are the two functions all the others are defined from, so the equation becomes purely algebraic.
4. Substituting a special angle only tests one value and never verifies an identity, which must hold across the whole domain.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_
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