How do you prove $tanx/secx + cotx/cscx = sinx+cosx$ ?

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Answer 1 · 2015-05-02T02:45:16

$(sin x/cos x).(cos x/1) + (cos x/sin x)(sin x/1) =$
$= sin x + cos x$

Answer 2 · 2016-08-25T10:22:52

See the Proof in Explanation.

$"The L.H.S."=(tanx+cotx)/(secx+cscx)$

$=(sinx/cosx+cosx/sinx)/(1/cosx+1/sinx)$

$={(sin^2x+cos^2x)/cancel((cosxsinx))}/{(sinx+cosx)/cancel((cosxsinx))}$

$=1/(cosx+sinx)$

$="the R.H.S."$

How do you prove tanx/secx + cotx/cscx = sinx+cosxtanx/secx + cotx/cscx = sinx+cosx?