PC 5.2 Notes – Verifying Trig Identities Solving an Equation: Use properties of equality to manipulate both sides of the equation to isolate the variable – the goal is to solve for x. Verifying an Identity: Starting with the expression on one side and through a series of steps involving identities or algebraic manipulations, convert that expression into the expression on the other side. EX 1: Multiply a) sin x (sin x - 2 ) b) ( 1 - cos x )( 1 + cos x ) c) (sin x + cos x ) 2 d) (2 tan x - 3 )(tan x + 1 ) EX 2: Factor a) cos 2 x - sin x cos x b) 1 - cos 2 x c) 2 cos 2 x + 5 cos x + 3 EX 3: Find LCD and combine sin 2 x a) + cos x cos x b) sin x cos x + cos x sin x EX 4: Rewrite as the sum of 2 fractions and simplify sin x - tan x cot x - 1 a) b) sin x cos x To verify: Assume NOT equal, then prove that they are Hints: Start with the most complicated side Know where you are going – keep the simpler side in mind Sines and cosines Algebraic manipulations, identities DO NOT: Add to BOTH sides Multiply BOTH sides Square BOTH sides
PC 5.2 Notes – Verifying Trig Identities EX 5: Verify a) csc(- x ) = - csc x c) cot 2 x - 1 = 1 - 2 sin 2 x 1 + cot 2 x b) tan x sin x + cos x = sec x d) 1 + sin x cos x +
= 2 sec x cos x 1 + sin x