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...

8 months ago

Answered by Bryan, an A Level Maths tutor with MyTutor

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


£24 /hr

Nathan L.

Degree: Materials Science (Masters) - Oxford, St Edmund Hall University

Subjects offered: Maths, Physics+ 1 more


“About Me: I'm a first year Materials science undergraduate at The University of Oxford. I loved learning about science and maths at school and hope my tutorials make you feel the same.  Structure: The key concept about tutorials i...”

£24 /hr

Jon S.

Degree: Economics & Bioscience (Bachelors) - Exeter University

Subjects offered: Maths, Economics+ 1 more


“I'm a first year student at Exeter University studying  Bioscience & Economics. I've enjoyed teaching for over a year now and I'm hoping my tutorials engage you with your subject, or at the very least help you get the grade you are lo...”

£20 /hr

Lewis M.

Degree: Biology (Masters) - Bristol University

Subjects offered: Maths, Biology


“About Me: I am a Biology student at Bristol University. I have always loved science and maths and I hope this will come across in my sessions! I have been invloved with tutoring for the majority of my school life, taking time out of ...”

MyTutor guarantee

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

How would you differentiate ln(sin(3x))?

What values of θ between 0 and 2π satisfy the equation cosec(θ) + 5cot(θ) = 3sin(θ)?

How do you intergrate sin^2(x)?

Find f'(x) and f''(x) when f(x) = 3x^2 +7x - 3

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