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:

link

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

£56

step-by-step explanation:

u divide 24 by 3 and u get 8 so if u do 8 time 7 or 8+8+8+8+8+8+8 u get 56 and 56 divided by 7 is 8.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.