Confirm Trig Identities with Factoring

Simplify: (secx-1)(secx+1)

Hint: you will need to FOIL first

• tan²x

• sinx

• cot²x

• cosx

Simplify:  tanxcotx-cos²x

• tanx

• cotx

• sin²x

• cos²x

• csc²θ
• sec²θ
• cscθ
• 1

• (cos/sin)(sin/cos)

• cos

• sin

• (sin/cos)(cos/sin)

Factor: sec²x − secx − 2

• (sec x)(secx − 2)

• (secx − 2)(secx − 1)

• (secx − 2)(secx + 1)

• (secx + 2)(secx − 1)

Organize this equation so it can be factored:

1−sin²x + sinx = 1

• move all to the right: 0 = sin²x − sinx

• cancel the ones and cancel a sinx

• replace sin²x with 1 − cos²x

• use this: 0 = sin²x − sinx + 2

Factor 0 = sin²x − sinx

• 0 = sinx(sinx)

• 0 = sinx(1 − sinx)

• 0 = cosx(sinx − 1)

• 0 = sinx(sinx − 1)

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔

Which of the following would be a step to prove the following identity?

• (1/ sin x) - (1 / cos x)

• (cos x - sin x) / ( sin x)

• (cos x - sin x) / (cos x)

• (1/ sin x cos x)