(tan/(1+sec)) + ((1+sec)/tan) = 2csc

(Show all work please.)

2 answers

I see tangents and secants on the left side, so I suspect to use the identity
tan^2x + 1 = sec^2x

LS
= tanx(1+secx) + (1+secx)/tanx
= (tan^2x + 1 + 2secx + sec^2x)/(tanx(1+secx))
= (sec^2x + 2secx + sec^2x)/(tanx(1+secx))
= (2sec^2x + 2secx)/(tanx(1+secx))
= 2secx(secx + 1)/(tanx(1+secx))
= 2secx/tanx
= (2/cosx)÷(sinx/cosx)
= (2/cosx)(cosx/sinx)
= 2/sinx
= 2cscx
= RS

Q.E.D.
y=2sec(1/3x)
Similar Questions
    1. answers icon 1 answer
  1. Find an equation for the tangent line to the curve at (π/2 , 2).y = 4 + cot(x) - 2csc(x) I am confused how to take the
    1. answers icon 2 answers
  2. Prove:sin^2(x/2) = csc^2x - cot^2x / 2csc^2(x) + 2csc(x)cot(x) On the right, factor the numberator as a difference of two
    1. answers icon 0 answers
  3. Solve (in radians) sec x = 2csc xWhen I work it out, it gets to 2cot x - 1 = 0 cot x = 1/2 Would it be ok to use tan^-1 (2) ? I
    1. answers icon 1 answer
more similar questions