Is 45p + 60r equivalent

2〖sen〗^2 x+3 senx+1=0

KonstantinChe [14]

2 sin²(x) + 3 sin(x) + 1 = 0

(2 sin(x) + 1) (sin(x) + 1) = 0

2 sin(x) + 1 = 0 OR sin(x) + 1 = 0

sin(x) = -1/2 OR sin(x) = -1

The first equation gives two solution sets,

x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ

x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ

(where n is any integer), while the second equation gives

x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ

2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0

2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0

(2 sec(x) + 1) (cot(x) + 1) = 0

2 sec(x) + 1 = 0 OR cot(x) + 1 = 0

sec(x) = -1/2 OR cot(x) = -1

cos(x) = -2 OR tan(x) = -1

The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives

x = tan⁻¹(-1) + nπ = -π/4 + nπ

sin(x) cos²(x) = sin(x)

sin(x) cos²(x) - sin(x) = 0

sin(x) (cos²(x) - 1) = 0

sin(x) (-sin²(x)) = 0

sin³(x) = 0

sin(x) = 0

x = sin⁻¹(0) + 2nπ = 2nπ

2 cos²(x) + 2 sin(x) - 12 = 0

2 (1 - sin²(x)) + 2 sin(x) - 12 = 0

-2 sin²(x) + 2 sin(x) - 10 = 0

sin²(x) - sin(x) + 5 = 0

Using the quadratic formula, we get

sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(x) + cot²(x) - 3 = 0

2 (cot²(x) + 1) + cot²(x) - 3 = 0

3 cot²(x) - 1 = 0

cot²(x) = 1/3

tan²(x) = 3

tan(x) = ± √3

x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ

x = π/3 + nπ OR x = -π/3 + nπ

7 0

2 years ago

decide whether enough information is given to prove that triangle XYZ is congruent to triangle JKL. If so, state the term you us

Dafna1 [17]

The information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.

<h3>The Triangle Congruence Theorems</h3>

Two triangles are congruent by the AAS congruence theorem if they both have two pairs of congruent angles and a pair of congruent non-included sides.
Two triangles are congruent by the ASA congruence theorem if they both have two pairs of congruent angles and a pair of congruent included sides.
Two triangles are congruent by the SAS congruence theorem if they both have two pairs of congruent sides and a pair of congruent included angles.

Thus, the information given to us shows that triangles XYZ and JKL is not enough to prove they are congruent by AAS, ASA, nor SAS.

Learn more about triangle congruence theorem on:

brainly.com/question/2579710