Verify if the following is true: 1/cos^2x+tan^2y = 1/cos^2y+tan^2x

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to prove that 1/cos^2x+tan^2y=1/cos^2y+tan^2x

Now 1/( cos x)^2 + ( tan y )^2 - 1/ (cos y)^2 - (tan x)^2

=> [(sin y)^2/ (cos y)^2] + 1/ (cos x)^2 - 1/ (cos y)^2 - [(sin x)^2/ (cos x)^2]

=> [1 - (sin x)^2]/ (cos x)^2 - [ ( 1 - (sin y)^2]/ (cos y )^2

we know that (sin x)^2 + (cos x)^2 = 1 or 1 - (sin x)^2 = (cos x)^2

=> (cos x)^2 / (cos x)^2 - (cos x)^2 / (cos x)^2

=> 1 - 1

=> 0

So 1/( cos x)^2 + ( tan y )^2 - 1/ (cos y)^2 - (tan x)^2 = 0

=> 1/( cos x)^2 + ( tan y )^2 = 1/ (cos y)^2 + (tan x)^2

Therefore 1/( cos x)^2 + ( tan y )^2 = 1/ (cos y)^2 + (tan x)^2.

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial