Find the solutions in the interval [0, 2π). (Enter your answers as a comma-separated list.)sec θ − tan θ = cos θ

The equation is an illustration of trigonometry ratios and identities

The solution in the interval  [0, 2π) is

The equation is given as:

In trigonometry identity, we have:

and

So the equation becomes

Multiply through by cosθ

In trigonometry,

So, we have:

Subtract 1 from both sides

Divide both sides by

Rewrite as:

Take arc sin of both sides

This gives

Read more about trigonometry ratios at:

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Step-by-step explanation:

Given the expression;

secθ − tan θ = cosθ

We are to find the solution in the interval [0, 2π).This is as shown;

From trigonometry identity;

secθ = 1/cosθ

tanθ = sinθ/cosθ

Substitute into the formula;

secθ − tan θ = cosθ

1/cosθ-sinθ/cosθ = cosθ

Multiply through by cosθ

1 - sinθ = cos²θ

1-sinθ = (1-sin²θ)

1-sin²θ-1+sinθ =0

-sin²θ+sinθ = 0

sin²θ = sinθ

sinθ = 1

θ = arcsin 1

θ = 90

θ = π/2

Hence the solution is π/2

step-by-step explanation:

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