Prove that #tan(x/2)+cot(x/2)=2cscx#?

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Answer 1 · 2017-08-01T16:40:20

#tan(x/2)+cot(x/2)=2cscx#

#tan(x/2)+cot(x/2)#

= #sin(x/2)/cos(x/2)+cos(x/2)/sin(x/2)#

= #(sin^2(x/2)+cos^2(x/2))/(sin(x/2)cos(x/2))#

= #1/(sin(x/2)cos(x/2)#

= #2/(2sin(x/2)cos(x/2)#

= #2/sinx#

= #2cscx#