simplify this (secx/cosx)-secxcosx?

5 Answers

• (secx/cosx) – (secx*cosx)

  = (secx*secx) – (1/cosx)*cosx

  = sec^2x – 1

  = tan^2(x)

• secx-cosx / tanx From trigonometry, secx=1/cosx Substitute: (1/cosx-cosx)/tanx [(1-cos^2x)/cosx]/tanx [sin^2x/cosx]/tanx tanx*secx/tanx secx The answer is secx

• = (sec x/cos x) – sec x cos x

  = ((1/cos x)/cos x) – (1/cos x)*cos x

  = 1/cos^2 x – 1

  = sec^2 x – 1 by pythagorean identities 1 + tan^2 x = sec^2 x

  = 1 + tan^2 x – 1

  = tan^2 x

• =>secx/cosx=sec^2x

  =>secxcosx=1

  So the above expression can be written as

  =>Sec^2-1

  =>tan^2(x)

• sec(x)/cos(x) = sec(x) * 1/cos(x)

  sec(x) = 1/cos(x)

  1/cos(x) * 1/cos(x) = 1/cos(x)^2

  sec(x) * cos(x) = 1/cos(x) * cos(x) = cos(x)/cos(x) = 1 if x%2pi =/= pi/2 or 3pi/2

  1/cos^2(x) – 1

  sec^2(x) – 1

  tan^2(x)