We have to find tan(x + x), given that sin x + cos x = 1.
We know that (sin x)^2 + (cos x)^2 = 1
sin x + cos x = 1
=> (sin x + cos x)^2 = 1
=> (sin x)^2 + (cos x)^2 + 2 sin x cos x = 1
=> 1 + 2 sin x cos x = 1
=> 2 sin x cos x = 0
=> sin 2x = 0
Now tan (x +x) = tan 2x = sin 2x / cos 2x
as sin 2x = 0
tan 2x = sin 2x/ cos 2x = tan (x +x) = 0
Therefore we prove that tan (x +x) = 0
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