Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

2cos² x = 2 - 3 sin x

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

cos 2x + 3 cos x + 1 = 0

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

sin 3x cos x - cos 3x sin x = (√3)/2

Determine whether the given identity is true or false. 

sec(θ) cot(θ) = sin(θ) +cot(θ) cos(θ)

Write the given trigonometric function in terms of $\cos x$.

$\csc x$

Is the given equation an identity?

$\frac{\sec^2x-1}{1+\tan^2x}=1-2\cos^2x$

Determine the exact value of the following expression by using a sum identity:

tan (7π/6 + 5π/3)

Under the given circumstances, determine the exact value of the expression provided: 

sin(A +B), sinA = -1/7, π < A < 3π/2 and cosB = -1/7, π < B < 3π/2

Write the following expression in terms of $\theta$ only. Use the identity for the cosine of a sum.

$\cos\left(\theta+\frac{\pi}{2}\right)$

Determine the exact value of the trigonometric function using the provided figure.

tan 2β

Determine the exact value of the expression using the provided data. 

sin 2β where cosβ = 84/85 β lies in quadrant IV.

Find the values of sin 2θ and cos 2θ if cos θ = -35/37 and sin θ > 0.