Posted by **Katherine** on Monday, February 21, 2011 at 9:44pm.

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

(Show all work please.)

- Pre-cal/Trig -
**Reiny**, Monday, February 21, 2011 at 10:27pm
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.

- Pre-cal/Trig -
**Delano**, Wednesday, November 2, 2011 at 4:44pm
y=2sec(1/3x)

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