If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).
2 answers:
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Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = (
) =
( or 60° )
Answer:
The correct options are: Option A, C and D
Step-by-step explanation:
We need to choose correct options by solving the given system of equations.
Let:
First Multiply equation 2 by 2 and add both equations.
Now, we will put value of x in equation 2 to find value of y
So, we get x = 3.14 and y = 2.14
Solution set is (3.14,2.14)
The given solution set (2,3) is not the solution of system of equations.
If we put x=2 and y =3 in the first equation:
(2,3) when substituted in the First equation the equation is True.
If we put x=2 and y =3 in the second equation:
So, (2,3) when substituted in the second equation the equation is false.
The correct options are: Option A, C and D