Trig Identities Proving (Trigonometric Identities Complete Guide!)

Become a master at proving trigonometric identities with this ultimate guide from Mario's Math Tutoring! This video tackles 20 diverse examples, providing you with essential tips, techniques, and strategies to simplify even the most challenging identity proofs. Perfect for students in trigonometry, pre-calculus, and calculus. We'll systematically work through problems, referencing key identities like: Reciprocal Identities Quotient Identities Pythagorean Identities (and their rearrangements) Co-function Identities Even and Odd Identities Learn powerful techniques such as: Starting with the more expanded side Converting to sine and cosine Finding common denominators Factoring (including difference of squares) Multiplying by the conjugate By the end of this video, you'll have the confidence and experience to tackle any trigonometric identity proof! Timestamps: 0:00 Introduction to Proving Trigonometric Identities 0:30 Tip 1: Start with the More Expanded Side 0:45 Example 1: Prove csc x - cot x cos x = sin x (Reciprocal, Quotient, Pythagorean Identities) 3:40 Example 2: Prove csc θ / (tan θ + cot θ) = cos² θ (Common Denominators, Division of Fractions) 7:50 Example 3: Prove csc θ / sin θ - cot θ / tan θ = 1 (Reciprocal, Quotient, Common Denominators) 10:30 Example 4: Prove sec² θ cot² θ - 1 = cot² θ (Reciprocal, Quotient, Pythagorean Identities) 12:30 Example 5: Prove cot² θ cos² θ = cot² θ - cos² θ (Pythagorean, Reciprocal, Distribution) 15:00 Example 6: Prove 3 cos(π/2 - θ) cot θ sec θ = 3 (Co-function, Reciprocal, Cancellation) 16:45 Example 7: Prove csc θ - cot(-θ) = sin θ / (1 - cos θ) (Even/Odd, Conjugate Multiplication) 21:50 Example 8: Prove cos x / (sin x + 1) + (sin x - 1) / cos x = 0 (Common Denominators, Pythagorean) 24:50 Example 9: Prove cos x - cos x sin² x = cos³ x (Factoring, Pythagorean Identity) 27:00 Example 10: Prove (cos² x + 3 cos x + 2) / sin² x = (cos x + 2) / (1 - cos x) (Factoring Trinomial, Difference of Squares) 31:30 Example 11: Prove (tan x - sec x)² + (tan x + sec x)² = 4 tan² x + 2 (Squaring Binomials, Combining Like Terms, Pythagorean) 35:30 Example 12: Prove sin x / (1 - cos x) - sin x / (1 + cos x) = 2 cot x (Common Denominators, Pythagorean) 38:50 Example 13: Prove sin x / (1 - cos x) - cot x = csc x (Common Denominators, Distributing Negative, Pythagorean) 42:00 Example 14: Prove (sec² θ - tan² θ) / (cot² θ - csc² θ) = 1 (Pythagorean Identities) 44:10 Example 15: Prove tan θ / (1 - sec θ) + (1 - sec θ) / tan θ = -2 csc θ (Common Denominators, Factoring, Conjugate) 49:20 Example 16: Prove sin θ / (1 - cos(-θ)) - cot θ = csc θ (Even/Odd, Conjugate, Common Denominators) 52:30 Example 17: Prove cot x / (csc x + 1) = sec x - tan x (Convert to Sin/Cos, Common Denominators, Conjugate) 56:30 Example 18: Prove tan⁴ x + 2 tan² x + 1 = sec⁴ x (Factoring Trinomial, Pythagorean) 58:00 Example 19: Prove cos^(2/3) x sin³ x + cos^(8/3) x sin x = (cos² x)^(1/3) sin x (Factoring GCF, Pythagorean) 1:00:30 Example 20: Prove sec⁴ x cot² x - sec² x tan⁴ x = 1 + csc² x (Factoring GCF, Difference of Squares, Pythagorean) ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join