Solve for 0=<x<360 : 2((tanx)^2) + ((secx)^2) = 1

First step I would take would make it look less intimidating by converting all components into sin and cos i.e

2(((sinx)/(cosx))^2) + 1/((cosx)^2) = 1

Notice that there is a common denominator of cosx^2    so I would multiply this up:

2((sinx)^2) + 1 = (cosx)^2

Eliminate cos by putting it in the form of sin using the trig identiy (cosx)^2 = 1 - (sinx)^2

so we have:

2((sinx)^2) + 1 = 1 - (sinx)^2

rearranging we obtain

3((sinx)^2) = 0

(sinx)^2 = 0

sinx = 0

In between 0 and 360, the sine function is 0 at 0 and 180 (360 is also a solution but not in the range)

so x = 0, 180

Bryan P. A Level Maths tutor, GCSE Maths tutor, Mentoring -Personal S...

1 year ago

Answered by Bryan, an A Level Maths tutor with MyTutor

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


£20 /hr

Rahul P.

Degree: Economics (Bachelors) - LSE University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I'm enthusiastic about Maths and I think my 598/600 UMS in Maths A Level puts me in a strong position to help others.”

MyTutor guarantee

£26 /hr

Priya L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“About Me: I recently graduated from the University of Warwick with an Economics degree. I am currently on a gap year before I begin my graduate role as a Management Consultant in October. I decided to tutor because I wanted to spend m...”

£20 /hr

Warren L.

Degree: Mathematics (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 6 more

Further Mathematics
English Literature

“Passionate maths and physics tutor from Cambridge university always ready to help students achieve their potential.”

About the author

£22 /hr

Bryan P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I am currently a BSc Mathematics student at the University of Bristol and I am already no stranger to teaching.I have worked as a teaching assistant in my secondary school's maths department where I also led one-on-one sessions with ...”

You may also like...

Posts by Bryan

Find the exact solution to: ln(x) + ln(7) = ln(21)

Solve for 0=<x<360 : 2((tanx)^2) + ((secx)^2) = 1

Write sqrt(50) in the form Asqrt(50) where A is an integer

Other A Level Maths questions

Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]

Derive from the standard quadratic equation, the form of the quadratic solution

Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.

How does one find the inverse of a non-singular 3x3 matrix A?

View A Level Maths tutors

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