Master fundamental trigonometric identities, sum and difference formulas, double-angle identities, and learn to simplify and transform trigonometric expressions.
Verify if the trigonometric identity is true!
Identity:
Simplify using trigonometric identities!
Expression:
The three main Pythagorean identities are:
Problem: Show that sin²(30°) + cos²(30°) = 1
Step 1: sin(30°) = 1/2, cos(30°) = √3/2
Step 2: sin²(30°) + cos²(30°) = (1/2)² + (√3/2)²
Step 3: = 1/4 + 3/4 = 4/4 = 1 ✓
Answer: Identity verified
Problem: Simplify: 1 - cos²θ
Step 1: From sin²θ + cos²θ = 1, we get sin²θ = 1 - cos²θ
Answer: 1 - cos²θ = sin²θ