Verify Trig Identities (Adv. Ex.)

Left

Right

Rewrite into sines and cosines

Combine fractions

factor common factor

multiply by the conjugate

Left

Right

Rewrite into sines and cosines

Combine fractions

factor common factor

multiply by the conjugate

Use a Pythagorean Identity

Left

Right

Rewrite into sines and cosines

separate fractions

factor common factor

multiply by the conjugate

Use a Pythagorean Identity

Left

Right

Rewrite into sines and cosines

separate fractions

factor common factor

multiply by the conjugate

Use a Pythagorean Identity

$$-\cos x$$

$$\cos x$$

1

$$\tan^2x$$

$$-\cos x$$

$$\cot^2x$$

1

$$\tan^2x$$

$$\csc x$$

$$\cot^2x$$

1

$$\sec^2x$$

$$2\sin^2x$$

$$\sin x$$

1

$$\sec^2x$$

Change everything to sines and cosines (reciprocal identities)

finding a common denominator

multiplying by the conjugate

squaring both sides

1: Find a common denominator to combine the fractions.

2: Combine the fractions.

1: Separate the fraction

2: multiply by conjugate

1: Change to sines and cosines

2: Combine fractions

1:Square both sides

2: Cancel common factors