MYTUTOR SUBJECT ANSWERS

467 views

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: 

[Tan^2x(1/sinx)]/sinx 

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

tan^2x/sin^2x

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

(sin^2x/cos^2x)/sin^2x

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. 

1/cos^2x=sec^2x

sec^2x=sec^2x

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

10 months ago

Answered by Mary, an A Level Maths tutor with MyTutor


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

334 SUBJECT SPECIALISTS

PremiumTimothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

£22 /hr

Lucy S.

Degree: Chemistry (Masters) - Durham University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Reading Chemistry at Durham University with expertise in Chemistry and Mathematics (A*A*) at GCSE/A-level”

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

About the author

£20 /hr

Mary B.

Degree: History (Masters) - Manchester University

Subjects offered:Maths, History+ 1 more

Maths
History
English

“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

How do I multiply two matrices together?

What is the factor theorem?

Let y=arcsin(x-1), 0<=x<=2 (where <= means less than or equal to). Find x in terms of y, and show that dx/dy=cos(y).

How do you differentiate 2^x?

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

mtw:mercury1:status:ok