Learning Resources

Focus D: Trident Fish

• Work with the most complex side of the equation first. Often, you can partially simplify one side, and then simplify the other side down to the same result.
• If the expression contains a binomial for which there is a formula, replace it with the corresponding monomial expression. Knowledge of the Pythagorean Identities will be necessary for this strategy.
• Try to rewrite expressions in terms of sine and cosine. Knowledge of the Reciprocal and Quotient Identities will be necessary for this strategy.
• Look for common factors in the given expression. Quite often, the proof can be less complex by simply first removing a common factor.
• The ability to simplify rational expressions will be an asset when proving trigonometric identities. You must know how to add, subtract, multiply and divide fractions.
• At times, you may have to multiply the numerator and denominator of an expression by the conjugate.