Mathematics, 14.10.2020 15:01 ejcastilllo

Please solve this question.

Answers: 2

Show answers

Answers

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

answer: at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

Answer from: Quest

3x + 4y -25 =0 represents the amount of change sianna should recieve

Another question on Mathematics

Mathematics, 21.06.2019 16:00

If f(x)= 3x+6 which of the following is the inverse of f(x)

Answers: 2

Answer

Mathematics, 21.06.2019 16:30

Arandom sample of 150 high school students were asked whether they have a job. the results are shown in the table. have a job do not have a job male 48 35 female 41 26 select a ord or phrase from the drop-down menus to correctly complete the statements describing the association.

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Two times a number plus three times another number equals 4. three times the first number plus four times the other number is 7. find the numbers

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Is the point (0, 8) on the x-axis or y-axis? how do you know?

Answers: 2

Answer

You know the right answer?

Please solve this question.
...