The identity `cos^4 x + 1 - sin^4 x = 2cos^2 x` has to be proved.

`cos^4 x + 1 - sin^4 x`

=> `(1 - sin^2 x)^2 + 1 - sin^4 x`

=> `1 + sin^4 x - 2*sin^2x + 1 - sin^4 x`

=> `2 - 2*sin^2 x`

=> `2(1 - sin^2x)`

=> `2*cos^2x`

**This proves that **`cos^4 x + 1 - sin^4 x = 2cos^2 x `

## 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