We have to prove that (tan t)^4 + (tan t)^2 + 1 = (1 - (sin t)^2* (cos t)^2) / (cos t)^4

The left hand side:

(tan t)^4 + (tan t)^2 + 1

=> (sin t)^4 / (cos t)^4 + (sin t)^2 / (cos t)^2 + 1

=> (sin t)^4 / (cos t)^4 + (cos t)^2*(sin t)^2 / (cos t)^4 + (cos t^4) / (cos t)^4

=> [(sin t)^4 + (cos t)^2*(sin t)^2 + (cos t^4)] / (cos t)^4

=> [ (sin t)^4 + (cos t )^4 + (cos t)^2*(sin t)^2]/(cos t)^4

=> [ ((sin t)^2 + (cos t)^2)^2 - 2*(cos t)^2*(sin t)^2 +(cos t)^2*(sin t)^2]/(cos t)^4

=> [ 1 - (cos t)^2*(sin t)^2]/(cos t)^4

which is the right hand side.

**Therefore we have proved that (tan t)^4 + (tan t)^2 + 1 = (1 - (sin t)^2* (cos t)^2) / (cos t)^4**

## 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

Already a member? Log in here.

Are you a teacher? Sign up now