How do you verify the identity $cotalpha+tanalpha=cscalphasecalpha$ ?

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Answer 1 · 2017-01-19T06:29:09

See proof below

$cos^2alpha+sin^2alpha=1$

$cotalpha=cosalpha/sinalpha$

$tanalpha=sinalpha/cosalpha$

$cscalpha=1/sinalpha$

$secalpha=1/cosalpha$

Therefore,

$LHS=cotalpha+tanalpha$

$=cosalpha/sinalpha+sinalpha/cosalpha$

$=(cos^2alpha+sin^2alpha)/(sinalphacosalpha)$

$=1/(sinalphacosalpha)$

$=cscalphasecalpha$

$=RHS$

$QED$

How do you verify the identity cotalpha+tanalpha=cscalphasecalphacotalpha+tanalpha=cscalphasecalpha?