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January 30, 2015

January 30, 2015

Posted by **Sharon** on Thursday, April 10, 2008 at 1:32am.

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

- Math -
**drwls**, Thursday, April 10, 2008 at 3:16amtan(x)/(1+sec(x))+ (1+sec(x))/tan(x)

= tan x/[(cosx+1)/cosx]

+ [(cosx+1)/cosx]/tanx

= sin x/(cosx+1) + (cosx +1)/sinx

= [sin^2 x + (cosx +1)^2]/[sinx(1 + cosx)]

= (sin^2x + cos^2x + 2 cos x + 1)/[sinx(1 + cosx)]

= 2 (1 + cosx)/[sinx(1 + cosx)]

= 2/sin x = 2 csc x

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