Mathematics, 14.10.2020 15:01 ejcastilllo

Please solve this question.

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Answer from: luis4921

see proof below

Step-by-step explanation:

Use the Cofunction Identity: sin (90 - A) = cos (A)

Use the Double Angle Identity: sin(2A) = 2 sinA cosA

Use the Triple Angle Identity: cos (3A) = 4cos³A - 3cosA

Use the Zero Product Property: If a · b = 0, then a = 0 or b = 0

Use Pythagorean Identity: cos²A + sin²A = 1 → cos²A = 1 - sin²A

Use Quadratic Formula: $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Proof LHS → RHS:

Assumption: Let A = 18°

Multiplication: then 5A = 5(18°)

→ 5A = 90°

Expand: 2A + 3A = 90°

→ 2A = 90° - 3A

Apply sin: sin (2A) = sin (90° - 3A)

Cofunction: sin (2A) = cos (3A)

Double Angle: 2 sinA cos A = cos (3A)

Triple Angle: 2 sin A cos A = 4cos³A - 3cos A

→ -4cos³A + 3cos A + 2sinA cos A = 0

Factor: cos A(-4cos² A + 3 + 2sin A) = 0

Zero Product Property: cos A = 0 or -4cos² A + 3 + 2sin A = 0

↓

Disregard (since cos A ≠ 0)

Pythagorean: -4cos² A + 3 + 2sin A = 0

→ -4(1 - sin² A) + 3 + 2sin A = 0

→ -4 + 4sin² A + 3 + 2sin A = 0

Simplify: 4sin² A + 2sin A - 1 = 0

a=4 b=2 c= -1

$\text{Quadratic Formula:}\qquad \sin A=\dfrac{-(2)\pm \sqrt{2^2-4(4)(-1)}}{2(4)}$

$=\dfrac{-2\pm \sqrt{4+16}}{8}$

$=\dfrac{-2\pm \sqrt{20}}{8}$

$=\dfrac{-2\pm 2\sqrt{5}}{2(4)}$

$=\dfrac{-1\pm \sqrt{5}}{4}$

$=\dfrac{ \sqrt{5}-1}{4}$

$\text{Substitute A = 18:}\qquad \sin 18=\dfrac{ \sqrt{5}-1}{4}$

Answer from: Quest

Ithink is the abswer b

Answer from: Quest

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is $3\times 8.50=$25.5$

cost of 2 dresses if one cost at $27.50 is $2\times 27.50=$55$

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is $25.5+$55+$17.50=$98

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