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

Answered by Mary B. Maths tutor

8407 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the cartesian equation for a curve written in parametric form?


Show that the derivative of tan(x) is sec^2(x), where sec(x) is defined as 1/cos(x). [Hint: think of tan(x) as a quotient of two related functions and apply the appropriate identity]


A cuboid has a rectangular cross section where the length of the rectangle is equal to twice its width x cm. THe volume is 81 cm^3. a) show that the total length L cm of the cuboid is given by L=12x+162/x^2


Integrate 1/((1-x^2)^(1/2)) by substitution


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences