Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

First, we need to realise that we will be using the trigonometric identity sin(x)2 + cos(x)2 = 1

As our goal is to end up with an equation involving only sin, we will therefore substitue cos(x)2 with ( 1 - sin(x)2 ), giving

5sin(x) = 1 + 2(1-sin(x)2)

We then expand the brackets, getting

5sin(x) = 1 + 2 - 2sin(x)2

We want the final equation to equal 0, so we add make 1+2 equal 3 and subtract it from both sides of the equation:

5sin(x) -3 = -2sin(x)2

we then add 2sin(x)2 on both sides, achieving the wanted equation:

2sin(x)2 + 5sin(x) -3 =0

Santiago G. GCSE Maths tutor, A Level Maths tutor, GCSE Spanish tutor...

5 months ago

Answered by Santiago, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


James T. GCSE German tutor, A Level Maths tutor, A Level German tutor...
View profile
£20 /hr

James T.

Degree: Mathematics with Study in Continental Europe (Masters) - Bristol University

Subjects offered: Maths, German


“Grammar school educated tutor studying Mathematics at the University of Bristol with experience in tutoring in Maths and German”

Dominique G. GCSE Classical Greek tutor, GCSE English Language tutor,...
View profile
£20 /hr

Dominique G.

Degree: Classics (Bachelors) - Cambridge University

Subjects offered: Maths, Latin+ 5 more

English Literature
English Language
Classical Greek
-Personal Statements-
-Oxbridge Preparation-

“Hi there! I'm Dommy, a third year undergraduate reading Classics at St. John's College, Cambridge and am currently on a year abroad at the University of Pavia, Italy. I am friendly and enthusiastic about learning and have previously t...”

MyTutor guarantee

Elakkeya J. A Level Biology tutor, GCSE Biology tutor, GCSE Chemistry...
View profile
£22 /hr

Elakkeya J.

Degree: Chemical Engineering (Masters) - Sheffield University

Subjects offered: Maths, Science+ 2 more


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

About the author

Santiago G. GCSE Maths tutor, A Level Maths tutor, GCSE Spanish tutor...
View profile
£20 /hr

Santiago G.

Degree: Computer Science with Management (Bachelors) - Edinburgh University

Subjects offered: Maths, Spanish+ 2 more


“Hi! I'm Santi, and I'm studying Computer Science with Management at the University of Edinburgh. I have always enjoyed subjects likemaths, physics and computing, andI'm here to help in any way possible with the questions you may have...”

MyTutor guarantee

You may also like...

Posts by Santiago

Find the positive value of x such that log (x) 64 = 2

Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

What is batch processing?

Other A Level Maths questions

Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Simplify (3x^2-x-2)/(x^2-1)

How do I solve an integration by substitution problem?

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss