6. Trigonometric Identities and More Equations

Find all solutions to the equation where 0 ≤ $\(\theta\)$ ≤ $2\(\pi\)$.

$\(\sin\]\theta\[\cos\]\left\)(2\(\theta\[\right\))-\(\sin\]\left\)(2\(\theta\[\right\))\(\cos\]\theta\)=\(\frac{\sqrt2}{2}\)$

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). 4 cos² x = 5 - 4 sin x

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin 2x = cos x

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). cos 2x + 5 cos x + 3 = 0

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin x + cos x = 1

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin 2x cos x + cos 2x sin x = √ 2/2

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). tan x + sec x = 1

Find one solution for each equation. Assume all angles involved are acute angles. cos(3θ + 11°) = sin( 7θ + 40°) 5 10

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

csc² θ ―2 cot θ = 0

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

2 tan θ sin θ - tan θ = 0

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

sec² θ tan θ = 2 tan θ

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

9 sin² θ ― 6 sin² θ = 1

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

sin² θ ― 2 sin θ + 3 = 0

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

cot θ + 2 csc θ = 3