Directions: Verify the given problems.
1. cos² θ + cos²(π/2 - θ) = 1
cos² θ + sin² θ = 1 1) The Cofunction Identities state that cos(π/2 - θ) equals sin θ so substitute
cos²(π/2 - θ) with sin² θ. (Sin² θ is used instead of sin θ because
cos(π/2 - θ) is squared.)
1 = 1 2) The Pythagorean Identities state that cos² θ + sin² θ = 1, so replace
✔ cos² θ + sin² θ with 1.
1. cos² θ + cos²(π/2 - θ) = 1
cos² θ + sin² θ = 1 1) The Cofunction Identities state that cos(π/2 - θ) equals sin θ so substitute
cos²(π/2 - θ) with sin² θ. (Sin² θ is used instead of sin θ because
cos(π/2 - θ) is squared.)
1 = 1 2) The Pythagorean Identities state that cos² θ + sin² θ = 1, so replace
✔ cos² θ + sin² θ with 1.
2. sin θ • csc(π/2 - θ) = tan θ 1) The Cofunction Identities state that csc(π/2 - θ) equals sec θ, so substitute
csc(π/2 - θ) with sec θ.
sin θ • sec θ = tan θ 2) The Reciprocal Identities state that sec θ equals 1/cos θ, so substitute
sec θ with 1/cos θ.
sin θ • 1/cos θ = tan θ 3) Multiply sin θ and 1/cos θ together.
sin θ/cos θ = tan θ 4) The Quotient Identities state that tan θ = sin θ/cos θ, so replace
sin θ/cos θ with tan θ.
tan θ = tan θ
✔
csc(π/2 - θ) with sec θ.
sin θ • sec θ = tan θ 2) The Reciprocal Identities state that sec θ equals 1/cos θ, so substitute
sec θ with 1/cos θ.
sin θ • 1/cos θ = tan θ 3) Multiply sin θ and 1/cos θ together.
sin θ/cos θ = tan θ 4) The Quotient Identities state that tan θ = sin θ/cos θ, so replace
sin θ/cos θ with tan θ.
tan θ = tan θ
✔
