sec^2(θ)-9=0

Solution

sec^{2} (θ) - 9 = 0

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

Solution steps

sec^{2} (θ) - 9 = 0

Solve by substitution

sec (θ) = 3, sec (θ) = - 3

sec (θ) = 3 : θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

sec (θ) = - 3 : θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

Combine all the solutions

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn, θ = arcsec (- 3) + 2 πn, θ = - arcsec (- 3) + 2 πn

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

2 cos^{2} (θ) = 2 - sin (θ)

cos (x + 1) = 0

sec^{2} (x) + tan^{2} (x) = 7

4 cos (x) = 1, 0 \leq x \leq 2 π

2 cos (2 x) + 4 sin (x) + 1 = 0