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November 21, 2014 Section 5.2 Verifying Trigonometric Identities Objective: Know how to verify trigonometric identities. x2 + 1 Expression x2 + 1 = 5 Equation (true for only some values in the domain) "Solve" x2 + x = x(x + 1) Identity (true for all real #s in the domain) "Verify" Note: There are no set techniques that you apply every time when verifying identities. Following are guidelines, which can be found on p.348 of the text...just guidelines! Work with only one side of the equation at a time. Usually it is better to start with the more complicated side first. Look for opportunities to factor an expression, add fractions, square a binomial, or create a single-term denominator. Look for opportunities to use the fundamental identities. Note which functions are in the final expression you want. Sine and cosine pair well, as do secant and tangent, and cosecant and cotangent. As a last resort, convert all terms to sine and cosine. Always try something! Even paths that lead to dead ends give you insight. November 21, 2014 Ex1: Verify the identity. a) sin2x - 1 = -cot x sin2x b) 1 1 = 2cot x sec x - 1 sec x + 1 2 2 c c) (1 + cot x)(1 - sin x) = cot x 2 2 Ex2: Verify these identities. 1 a) sec u + tan u = sec u - tan u b) cot t cos t = csc t - sin t c) 1 - sin x cot2x = 1 + csc x sin x 2 Mo re! November 21, 2014 Try this one! sin x (csc x - 1)(csc x + 1) = 1 - sin x 2 2