To solve the system of equations, we will first simplify the given equations:
1) 4tgx + 3ctgx = 7 tgx and ctyx are reciprocals of each other. Therefore, we can rewrite the equation as: 4tgx + 3/tgx = 7 Solving for tgx term: (4tgx)^2 - 7(4tgx) + 3 = 0 Let y = tgx Substitute: 4y^2 - 7y + 3 = 0 Solving the quadratic equation, we get: y = 1 or y = 3/4 Therefore, tgx = 1 or tgx = 3/4
2) sin3x + sin7x = -2 sin(3x) + sin(7x) = -2 This is a trigonometric equation and does not have a straightforward solution with the given information. More information or assumptions are needed to solve this equation.
Therefore, the values of tgx can be 1 or 3/4, but the solution for sin3x + sin7x = -2 cannot be determined without additional information.
To solve the system of equations, we will first simplify the given equations:
1) 4tgx + 3ctgx = 7
tgx and ctyx are reciprocals of each other. Therefore, we can rewrite the equation as:
4tgx + 3/tgx = 7
Solving for tgx term:
(4tgx)^2 - 7(4tgx) + 3 = 0
Let y = tgx
Substitute:
4y^2 - 7y + 3 = 0
Solving the quadratic equation, we get:
y = 1 or y = 3/4
Therefore, tgx = 1 or tgx = 3/4
2) sin3x + sin7x = -2
sin(3x) + sin(7x) = -2
This is a trigonometric equation and does not have a straightforward solution with the given information. More information or assumptions are needed to solve this equation.
Therefore, the values of tgx can be 1 or 3/4, but the solution for sin3x + sin7x = -2 cannot be determined without additional information.