8-4 Relationships among the functions

Use the formulas(on page 317)

Steps to be loosely followed

1. Algebra

2. Identities – try Pythagorean, then move everything to sin and cos if that helps

3. Algebra

4. Continue steps 1-3

Ex 1. Secx - sinxtanx s^2+c^2=1 c^2=1-s^2

1/cosx - sinx(sinx/cosx)

1/cosx - sin^2x/cosx

1-sin^2x/cos x

cos^2x/cosx = cosx

Ex 2. Verify that tanxsinx + cosx = secx

sinx/cosx(sinx) + cosx

1/1 x sin^2x/cosx+cosx/1 x cosx/cosx

Sin^2x/cosx + cos^2x /cosx = sin^2 + cos^2x/cosx = 1/cosx = secx

Ex 3. Cos^2x(tan^2x + 1)

Cos^2x(sec^2x)

Cos^2x(1/cos^2x) = 1

Ex 4. Sinx/cosxtanx

Sinx/cosx(sinx/cosx)

Sinx/sinx = 1