Given a point P (x, 3) (x ≠ 0) on the terminal edge of angle θ, and cos θ = √ 10 / 10 times x, the values of sin θ and Tan θ are obtained Please explain the difficulties when solving the problem. Thank you

Given a point P (x, 3) (x ≠ 0) on the terminal edge of angle θ, and cos θ = √ 10 / 10 times x, the values of sin θ and Tan θ are obtained Please explain the difficulties when solving the problem. Thank you

Tan θ = 3 / X (P can be regarded as the first quadrant, which does not affect the calculation results);
sinθ=tanθ*cosθ=(3/x)*(x*√10/10)=3√10/10；
cosθ=±√(1-sin²θ)=±√(1-90/100)=±√10/10
Tan θ = sin θ / cos θ = (3 √ 10 / 10) / (± 10 / 10) = ± 3

Given that there is a point P (x, 2x-3) on the terminal edge of angle θ, and Tan θ = - x, try to find sin θ + cos θ,
Given that there is a point P (x, 2x-3) on the terminal edge of angle θ, and Tan θ = - x, try to find the value of sin θ + cos θ

(2x-3)/x=tanθ=-x
x=1 or -3
When x = 1:
P(1,-1)
∴sinθ+cosθ=0
When x = - 3
P(-3,-9)
Ψ sin θ + cos θ = 2 (radical 10) / 5
Maybe so

If two of the equations MX ^ 2 + (2m-3) x + m-2 = 0 (M is not equal to 0) are Tana and tanb respectively, find the value of Tan (a + b)

Tana * tanb = (m-2) / m, Tana + tanb = (3-2m) / m, Tan (a + b) = (Tana + tanb) / (1-tana * tanb) = (3-2m) / (M - (m-2)) = (3-2m) / 2 because the equation MX & # 178; + (2m-3) x + (m-2) = 0 (M & # 185; 0) has two real roots (2m-3) ^ 2-4m (m-2) > = 0 4m ^ 2-12m + 9-4m