1: This is a quadratic equation in terms of sin(x): 7(sin(x))^2 + 5sin(x) - 2 = 0. You can solve this by letting sin(x) = u and then solving for u, and then finding the corresponding x values.

2: This is a quadratic equation with both sin(x) and cos(x) terms. You can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to express everything in terms of sin(x) or cos(x), and then proceed to solve.

3: This is a quadratic equation in terms of tangent and cotangent. You can rewrite tan(x) as sin(x)/cos(x) and cot(x) as cos(x)/sin(x), and then solve as you would a regular quadratic equation.

4: This is a trigonometric equation with both cosine and sine terms. You can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to express everything in terms of one trigonometric function, and then solve.

5: This is a quadratic equation in terms of sin(x). Factor out sin(x) to solve for the values of x.

6: This equation involves both cosine terms. You can use the sum-to-product identity to simplify the equation and then solve for x.

7: Factor out sin(2x) to simplify the equation and solve for the values of x.

8: This equation involves both sine and cosine terms. Rewrite the equation in terms of only one trigonometric function and then solve.

9: This equation involves both cosine and sine terms. Use the Pythagorean identity to simplify the equation and then proceed to solve.

10: This equation involves both cosine and sine terms. Rewrite the equation in terms of only one trigonometric function and then solve.