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

MB
Answered by Mary B. Maths tutor

8537 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the integral of x^2 + 3x + 7?


Find the integral of (sinxcos^2x) dx


The circle C has centre (3, 1) and passes through the point P(8, 3). (a) Find an equation for C. (b) Find an equation for the tangent to C at P, giving your answer in the form ax + by + c = 0 , where a, b and c are integers.


The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).


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