Solving trig equations?

Question

I need to solve these equations and list all of the solutions. Please show steps and explain

1. 3sec^2 θ-4 = 0

2. sin^2 θ = 3 cos^2 θ

3. 2sin^2 θ = 2 + cos θ

Answer 1

1.given equation is  3sec^2 θ-4 = 0

Add 4 to each side

3sec^2 θ-4 +4 = 0 +4

3sec^2 θ= 4

Divide each side by 3

3sec^2 θ /3= 4/3

sec^2θ = 4/3

sqrt the each side

sqrt (sec^2θ =sqrt 4/3

secθ =2/sqrt(3)

secθ=sec30degrees

    θ=30 degrees 

Comments

Thank you!!! what is sqrt?

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sqrt means squareroot.

Answer 2

2. sin^2 θ = 3 cos^2 θ

Divide each side by cos^2θ

 sin^2 θ/cos^2 θ = 3 cos^2 θ/cos^2 θ

 tan^2θ =3         ( sin^2 θ/cos^2 θ= tan^2θ)

sqrt each side

 sqrt tan^2θ =sqrt 3 

        tanθ =   tan60 degrees

            θ=60 degrees