Question: i) Show that the equation 2 sin x cos x = 1 can be written as a quadratic equation in cos x. ii) Solve

i) Show that the equation 2 sin² x − cos x = 1 can be written as a quadratic equation in cos x.

ii) Solve the equation 2 sin² x − cos x = 1 for 0° ≤ x ≤ 180°.

iii) Hence solve the equation

2 sin 20 cos X 2 = 1


for 0° ≤ x ≤ 180°.

2 sin 20 cos X 2 = 1

Step by Step Solution

★★★★★

3.40 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

i Using the identity sin x cos x 1 we can rearrange the given equation as 21 cos x cos x 1 Expanding ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Complete Pure Mathematics Questions!

Q:

i) Show that the equation 2 tan x = cos x can be written as a quadratic equation in sin x. ii) Solve the equation 2 tan x = cos x for 0 x 180. iii) Hence, state the set of values of x for which 2...

Q:

= Suppose you hold a long-horizon investment for H years and the H-period return WH (1 + R) (1 + R) ... (1 + R). Assume that the continuously compounded return r = ln(1 + Rt), is independent and...

Q:

1. 3 2 Consider the function f(x) = x - 3x - 9x + 10, x (a) . Find the equation of the straight line passing through the maximum and minimum points of the graph y = f(x). (4) (b) Show that the point...

Q:

doublePendulum v0.6 written by Alexander Erlich (mailto:alexander.erlich@gmail.com) Last update submitted to MATLAB File Exchange on October 5th, 2010. Lagrangian and di\u001berential equations The...

Q:

7-9 Precalculus. Please put the answer in proper format. The following equation involves a trigonometric equation in quadratic form. Solve the equation on the interval [0,2x). 4 cos *x - 3 =0 What...

Q:

doublePendulum v0.6 written by Alexander Erlich (mailto:alexander.erlich@gmail.com) Last update submitted to MATLAB File Exchange on October 5th, 2010. Lagrangian and di\u001berential equations The...

Q:

ue.1[A] Answer the following multiple choice questions.(K/U) 1. Which is the second derivative of the function y= -cos x with respect to x? a. d ^2y/dx^2=sinx b. d ^2y/dx^2=-sinx c. d ^2y/dx^2= cosx...

Q:

Question 9 Solve the given differential equation by variation of parameters. y" + y = sec x Hint: Use the following formula Y = - yu + y,uz = -y1 dx + 2.J dx P W W O y (x) = c 1 cos x + C 2 sin x +...

Q:

17. Let f (x) =- X SHORT ANSWER, with work required to be shown, as indicated. 12 -4 (a) State the domain. Answer. 18. Find the equation for a line which passes through the points (9, -5) and (3, 1)....

Q:

This is Calculus and vector course for grade 12 high school. Those are the questions I need help with and I also attached photo of formula sheet in case you need it as a reference. Those are two...

Q:

Section 1.4 We only know one point on the tangent line; therefore, determining the slope of the tangent line is not as straight- forward as determining the slope of the secant line (of which we know...

Q:

Financial Statement Given the Financial Statement information listed below: Balance Sheet A = Asset Last name: 1. Prepare an Income Statement. Balance Sheet L= Liability 2. Prepare a Balance Sheet....

Q:

Describe New Zealand's foreign exchange rates and how those rates could impact Walmart's future financial performance. Be sure to address: interest rates, balance of payments, government policies,...

Q:

Calculate all three total differential operations of the function f(x1, x2, x3) = x1(x2 x3) x1(x2 x3) (4.1) and verify relation (4.2) of [18]. 3 Calculate the total differential dxf(x) by means of...

Q:

What will be the result if we conclude that the mean is 45 when the actual mean is 50? (i) We have made a type I error. (ii) We have made a type II error. (iii) We have made the correct decision....

Q:

Which of the following sample results yields the smallest p-value and why? (i) x = 28, s = 6 (ii) x = 27, s = 4 (iii) x = 32, s = 2 (iv) x = 26, s = 9 Suppose we wish to test H 0 : = 30 vs. H 1 : ...

Q:

Suppose we identify 50 women 50 to 54 years of age who have both a mother and a sister with a history of breast cancer. Five of these women themselves have developed breast cancer at some time in...

Q:

Acme Company has two divisions, East Division and West Division. During the current year, the East Division has sales of $ 9 0 0 , 0 0 0 , a turnover of 1 . 5 0 , a return on investment of 1 2 % ,...

Q:

*SHOW ALL CALCULATIONS* PR 8-2A Aging of receivables; estimating allowance for doubtful accounts Obj. 4 Trophy Fish Company supplies flies and fishing gear to sporting goods stores and outfitters...

Q:

Connie's Bistro, Inc. reported the following information about its long - term debt in the notes to a recent financial statement ( in millions ) : Long - term debt consists of the following: December...