Using Trigonometric Identities prove that [(tan^2x)(cosecx)]/sinx=sec^2x

You should begin by identifying all the Trigonometric Identities that may be useful in this problem. Specifically, cosecx=1/sinx tanx=sinx/cosx 1/cosx=secx and possibly tan^2x + 1= sec^2x. I began by changing cosecx into 1/sinx in hopes of simplifying the fraction: 


I then simplified the fraction by multiplying the reciprocal of the top fraction (sinx/1) by the numerator and the denominator. This gave me:


I then substituted tan^2x in the numerator for the alternate sin^2x/cos^2x giving me:


Then I simplified the fraction multiplying by the reciprocal of the denominator (1/sin^2x) to both the numerator and the denominator of the fraction.

The denominator canceled out and both of the sin2^x cancel out in the numerator leaving me with 1/cos^2x which also equals sec^2x, completing the proof. 



Mary B. GCSE History tutor, IB History tutor, A Level History tutor, ...

1 month ago

Answered by Mary, an A Level Maths tutor with MyTutor

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


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

Mary T.

Degree: Mathematics (Masters) - Durham University

Subjects offered: Maths


“About me: I am currently studying maths in my first year at Durham University. Not only do I have a love for my subject but also for teaching it. In my last year of sixth form I set up a school wide tutoring system which helped many ...”

Sadhira W. GCSE Maths tutor, GCSE Biology tutor, GCSE Chemistry tutor...
View profile
£20 /hr

Sadhira W.

Degree: Biomeical Engineering (Masters) - Imperial College London University

Subjects offered: Maths, Physics+ 1 more


“Due to the diversity of my course, I have maintained high proficiency in all four fields (Maths, Physics, Biology, and Chemistry) that I tutor in, something most cannot claim once they have left school, building further on each of them...”

MyTutor guarantee

PremiumJoe C. A Level Maths tutor, GCSE Maths tutor
View profile
£24 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

About the author

Mary B. GCSE History tutor, IB History tutor, A Level History tutor, ...
View profile
£20 /hr

Mary B.

Degree: History (Masters) - Manchester University

Subjects offered: Maths, History+ 1 more


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

MyTutor guarantee

You may also like...

Posts by Mary

Using Pythagoras Theorem find the length of the hypotenuse of a right triangle where a=7 cm and b=11 cm. Round to the nearest tenth

Using Trigonometric Identities prove that [(tan^2x)(cosecx)]/sinx=sec^2x

What is the difference between primary and secondary sources and when should they be used?

Other A Level Maths questions

What is the chain rule, product rule and quotient rule and when do I use them?

Factorise x^3-6x^2+9x.

If y = 2^x, find dy/dx

How to sum an arithmetic progression?

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